ΔV is a hard sci-fi game, which means it attempts to obey physics as much as possible. This means a lot of the gameplay will feel quite different to many other space games, even ones which claim to use realistic physics. For example all engines use propellant, there are no force fields, and so on.
You will need to keep an eye on your speed. When driving a real car, going everywhere at full throttle will lead to you hitting things, and the same is true here. Ships in ΔV are built tough, they are industrial machines not racing pinnaces, but they have their limits. Until you're fairly familiar with how long it takes to stop and turn, we advise taking it fairly slow and giving yourself plenty of time to react to what's going on around you. Remember, this is space and once you're moving at all you'll drift forever, so you can take as much time as you need!
The K37 and other ships you'll fly in ΔV are very robust and while they can be disabled, it's very difficult to destroy them. Don't expect your ship to explode if you tap a rock, and don't expect other ships to explode just because you poked a mass driver round into them. Most of the time, you will find that your ship's onboard systems such as the reactor and thrusters will be rendered inoperable long before the hull itself breaks, and most damage just results in your ship being dead in the water (so to speak), at which point you will be rescued by your friendly neighbourhood recovery ship. The first thing you're likely to do in your first flight is ignore the earlier advice to take it slow and steady, so you'll immediately crash into loads of rocks.
Most of the time, crashing your ship into stuff will have one or two effects. In almost all cases, the sudden high-gee acceleration of the crash will cause damage to your reactor's control systems, which will make it more sluggish at controlling its own temperature. This generally isn't a huge problem, as the reactor runs fairly cool by default and has enough headroom to spike up in temperature quite a lot before anything nasty happens. If this damage is severe enough though, the reactor can become almost totally unable to control its own temperature, so if you've crashed a lot you should probably pay attention to your reactor temperature.
The second common form of damage caused by crashing is to your thrusters. Every thruster has a nozzle, and smashing space rocks into your thrusters' nozzles usually isn't very good for them. Thrusters can be damaged in a few different ways, but most common in collisions are misalignment and choke. Misalignment represents damaged thruster mounts and causes a thruster to fire in the wrong direction. Small amounts of misalignment don't really affect flyability very much, but extreme misalignment will - in short - cause the ship to behave weirdly. Strafing left may also push you backwards and cause some rotation, for example. Besides misalignment, a thruster that's had asteroids smash into it may also become choked. Choke damage represents the thruster's nozzle being jammed with asteroid debris, and reduces thrust.
Repairing and managing damage
You can jury-rig your ship's systems in-flight to try and control damage. You can't actually repair damaged components without repair drones, but you //can// trade off one form of damage for another. For example, a thruster that is completely choked but is aligned correctly and unworn can be jury-rigged through the onboard maintenance system to unchoke it at the cost of misaligning and wearing it out slightly.
General earlygame strategy
You can hire Crew from the crew menu at Enceladus station. A geologist is required to identify the mineral content of chunks outside of your cargo hold and estimate the value. this is the most important crewmember for early game (pre-MPU) for detecting high-value chunks to chase after.
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 MPU allows you to process chunks (by blasting the ice out of it) and store the processed minerals. Each ship has a specific quantity of processed minerals it can hold, which can be improved with the cargo container.
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.
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.
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.
Uncategorised other stuff
Ultimately, all of the power your ship uses comes from heat in your reactor. Even electrical items like mining lasers which are powered by your onboard turbogenerator ultimately use reactor heat, as the turbine is powered by high temperature, high pressure steam tapped from the reactor, just as in real power plants.