Welcome to Delta-V!
On your first dive, focus on making profit and running from hostile ships, you're a fresh miner after all, not a warship, and like the tutorial tip says, don't push the velocity too high, you don't want to impact against asteroids at high speeds, as the repair bill may be overwhelmingly high if it's a bad hit. And finally keep an eye on your propellant, you don't want to be dead in the water and need Search and Rescue (SAR) to have to bail you out.
Controlling the Ship Efficiently
The autopilot is great, but usually expends a lot of extra effort keeping precise control over the ship's movement. When such accuracy isn't needed, it is often more efficient to manually perform "close enough" maneuvers. Don't be afraid to waste a bit of propellant to test your controls and rebind them to something more comfortable, many people go back and forth on whether rotate should be A and D, or Q and E on a QWERTY keyboard, it's all up to choice and preference, and will save fuel in the long term, even on your first dive.
Things to Look For
If you find a lifepod, those entities are usually very safe early game paydays, and a good jumpstart for your income, but otherwise look for any bright blue ore chunks, as these are beryllium chunks, and are the easiest to identify as valuable at a glance.
If you really want to try to be smart, go for wolfram (Aka: Tungsten) chunks and see what the interior cargo bay readout says about any chunks you take in, if the chunk is more water than wolfram, then try to navigate that chunk out of your system. If the chunk has more wolfram than water, keep it, as wolfram chunks have incredibly high metal quantities per ore chunk, and likely have a high value per ore chunk.
If you really feel confident in your ship to ship abilities, you can try to destroy a pirate for an early bounty, or tag along with a bounty hunter for an early pod acquisition, but this is not advised, as it is incredibly easy for something to go wrong, for only around 50-150K credits. If you don't want the pirate ship, but just want the lifepod, and the reactor on the pirate ship cools down completely to the point where your mass driver doesn't damage the ship any further, you have your main torch.
Things to do at Enceladus Station
Crew Management
Back at station, you usually want a full crew first and foremost, one for each type, as each crew member's pair of abilities are incredibly helpful.
The pilot Augments (Via education) and automatically triggers your adrenal slowdown (Via experience) when a collision is imminent, this adrenal slowdown can give you time to react to an oncoming disaster, whether to attempt to evade the target and prevent the collision entirely, or to face it in an attempt to destroy it and mitigate the damage. The increased adrenal slowdown also allows you to more precisely line up your shots or ore acquisition, which can make capturing high speed ore much easier.
The mechanic is not absolutely necessary during a flight, however in a practical sense they are highly necessary, as they allow you to jury-rig systems to mitigate mid-flight damages (Via education), as well as repair high damage, high price components to a better condition (However it is ill advised to repair low damage or low price components, as replacing can often be cheaper both money-wise and time-wise for those particular components, this is done via experience).
The geologist will attempt to estimate the value of ores around you (Via experience), and attempt to accurately estimate the mineral market's valuation (Via education). This becomes less important once you obtain a Mineral Processing Unit (More on that later), but it is especially important early-game, as ore capacity is highly limited.
The astrogator will mark out potential ship contacts (Via education) with a red circle around bright LIDAR contacts, while also keeping track of Points of Interest in the ever-shifting rings (Via experience). Possible contacts may be false positives of tightly clumped ores, but being able to react to a hostile contact early can make the difference between escaping with your life, getting the first shot on a hostile, or getting a critical reactor failure and winding up drifting in a lifepod yourself.
Ship Equipment
In terms of ship equipment, more expensive components aren't necessarily the best, especially in the main torch and Reaction Control System (RCS) departments, each component has it's ups and downs. Be sure to read the statistics of each system, located in the bottom-right of the simulation screen, which it's self is located at the top of the menu, as well as the description for each system, located at the top of the simulation screen upon clicking on the component.
It is strongly advised to have at least one weapon for self-defense, and it is mildly advised to have one weapon for mining, but remember that the high stress centerline mount can mount some specialized pieces of equipment that the two low stress mounts can not, and that you can use your RCS for mining if absolutely necessary.
With all systems, it is also advised to generate enough power to run at least that system in isolation without interruption, which is determined by reactor heat (More on that later), your turbine, and your Auxiliary Power System (APS), versus your power and thermal draw of desired system.
The Mineral Processing Unit (MPU) is the next noteworthy component, and it is highly advised to get one as soon as possible in the "Cargo bay" tab. A MPU can increase your effective fuel range, and effective cargo capacity, by converting the ice on asteroids into propellant (If possible, some MPUs can not do this), and moving the leftover ore into the ship's onboard processed cargo bay. However MPUs are not perfectly efficient at either of these actions, and have a limited area that they can affect in the cargo bay.
Autopilots behave in different ways, and no singular autopilot can be considered "perfect", with preference ultimately being determined by the ship build and person using them, experiment! Worst case scenario it's good to practice flying manual.
All other systems are relatively self-explanatory, and/or are able to be discerned from their descriptions alone.
Ship Tuning
The tuning menu is where most people personalize their ships above and beyond just the components, and it is important to at least look through the menu once before diving a second time. Much like the equipment tab, descriptions of what tuning each item does appear at the top. Uptuning the engine increases the propellant usage and thrust in a 1:1 ratio, but increases the wear on the engines logarithmically, meaning at a faster rate than just 1:1, so it is ill advised to uptune the engines unless you either need the thrust, the engines are cheap, or you're willing to replace them every so often.
Higher powered weapons draw more power, and send off ore chunks at a faster rate (Thus making them harder to acquire), but also break asteroids faster, and are better for ship to ship combat. A hotter reactor will generate more power, but is also at a higher risk of melting down for any reason, so if you need a bit of extra power, but can't afford a new turbine or APS, it's good to run the reactor slightly hotter, however overdoing this can lead to total ship loss. The autopilot settings are all explained, and all up to preference, much like the autopilot it's self.
Ship Repairs
The repair menu is relatively simple, with the system and damages on the left, and the options for fixing these damages on the right. Replacing cheap systems can often be cheaper than repairing them, but repairing expensive systems, even if you plan on replacing them, especially when the system is heavily damaged, is far cheaper than simply replacing them. The price the old system would go for is factored into the replacement cost as well.
Launching a new Dive
When you're ready to dive again, you can plan the next dive's location, how precise you want the dive to be, and how many supplies to replenish. It is highly advised to completely fill up your propellant until you're more experienced, even more experienced pilots can run out mid-flight in good conditions.
Basic Advice
General
First and foremost, get a full crew, education trains up slowly over in-game time while at station, and experience trains up on the field.
Get a self-defense weapon, a mining weapon, and the manipulator arm, the arm will let you salvage derelicts with a guaranteed chance, and the self-defense weapon combined with it will let you salvage pirate ships.
Upgrade your power system to keep pace with the new heightened draw, at least for short bursts. If it isn't broke, don't fix it, get more of it!
A Mineral Processing Unit should be your next step after your weapons and power system are in place.
Adjust your engines and handling while upgrading, see what you like and what you don't. A fuel tank it's self has no weight, it's just the propellant inside that has the weight, so don't be afraid to buy an extra large tank, but leave it empty.
And finally, flying manual is the most efficient if you're absolutely precise, which is a tall order, while flying with autopilot has absolute precision based on the settings you set, but will likely waste some fuel on frivolous maneuvers, try flying a hybrid of the two instead.
Mining
Pre MPU mining
Without an MPU (Mineral Processing Unit), the amount of material you can return with is limited by the number of chunks that will fit in your cargo bay. The Geologist is the most important crewmember at this stage, where estimating the content of chunks will allow you to maximize the value of your cargo bay.
MPU mining
The MPU allows you to process chunks (by blasting the ice out of it), removing the refined minerals from the cargo bay and pulling them into the ship's internal stores. Each ship has a specific quantity of processed minerals it can hold, which can be improved with the cargo container.
Salvage
Occasionally, you will come across a Derelict ship. If you have an AR-1500 Manipulator mounted on your high-stress hardpoint, you can tow the ship back to Enceladus. Otherwise, approaching the ship will give a dialogue option to send a crewmember over with some remass for an attempt to bring it back online. This has a chance of causing an explosion and putting the crewmember on leave for some time.
Combat/Salvage
Combat
Space pirates. Whether you hate them or are one of them, combat is something that you will come across when playing for any significant length of time. Pirate ships are generally identified by the lack of an iff transponder. Most pirates will request money, some will attack immediately. Approaching hostiles will trigger the dangerous situation ambient effects: red highlights around the screen and more intense music. Skilled astrogater crewmembers will mark ship lidar contacts with red circles, making pirates easier to locate.
Pursuing Combat
Astrogating to a claim beacon has an increased chance of spawning any npc encounter. Occasionally you will come across an npc claiming to be bounty hunting. Asking to join them will usually spawn a hostile encounter soon.
Damage Types
Kinetic: Pokes holes in enemy ships causing damage and fuel leaks. Kinetic Laser: Pulse lasers tuned to lower frequencies will act as an intermediate step between kinetics and thermals. Thermal laser: Transfers heat to target. Can quickly overheat reactors if aimed properly. Microwave: Shuts down ship computers with emp.
Destroying Ships
Ships will be destroyed when the reactor explodes. This can be achieved using sheer damage to cause fuel rods to jam or by using thermal weapons to overheat them. Remember that the most powerful weapon available is usually the main drive thruster on your ship. Destroyed ships will spawn a life pod that can be returned to Enceladus for 50,000-150,000.
Disabling Ships
Ships will become disabled when they lose all of their fuel. Most ships will begin leaking fuel when subjected to kinetic impacts, particularly near the reactor. A majority of ships will be disabled by microwave emp. Some will not, and will require additional effort to defeat. Most pirates will begin fleeing after a certain damage threshold.
Combat Salvage
Disabled ships can be salvaged like derelicts. Combat salvage usually has a lower value than derelicts due to damage. Values generally hover around 350,000, varying with ship equipment and damage.
Common Points of Interest
Obonto stations
Obonto stations found in the belt will buy common refined minerals for 2-6 times market price. Individual stations will only buy one mineral per dive, and can ask for iron, platinum, palladium, or vanadium.
Phage stations
Phage stations found in the belt will sell fuel for "belt rate". Usually more efficient to fit a larger fuel tank and purchase from the dive menu [E'].
Space Bar
Drinks at the space bar can improve crew mood.
Moonlet
Can sometimes contain uranium caves, otherwise just an astrogation target.
Uranium Caves
Contains several uranium crystals worth 10,000e. Found inside some moonlets.