Introduction
Pirates are ships that don't have transponders, and will usually attack you on sight. If they blow up, you can recover an escape pod and turn it in for money. However, you should instead attempt to recover the ships themselves. They can be sold or patched up for use yourself.
Required Equipment
The manipulator arm is the best way to recover enemy ships. A TNTRL is capable of recovering pirate ships, but ships with diagonal forward RCS are a lot better. These include the KTA24 or the Vulture Prospector. For weapons, any mass driver will do, with the railgun being the best, and also a microwave gun.
Events that Summon Pirates
The most common event that summons pirates is an NPC approaching you to warn you about either ships without transponders, or ships with leaking reactors. If you respond that you are here for a combat patrol, or that you have seen ships with no transponders, it will summon some pirates to fight.
Other events that can summon pirates are a ship fighting a pirate, or just a lone pirate coming to ransom you.
The amount of money in your bank account influences what sort of pirates appear. A 4 million bank balance spawns much more valuable pirates than a zero bank balance.
How to Disable Pirates for Recovery
Now comes the fun part. When you get a pirate in your sights, turn off your manipulator and railgun and start microwaving them. Keep the microwave trained on the enemy ship and they should start drifting. When the back of the ship comes into view, turn on the railgun for a second and try to punch a hole in the reactor. It is easy to over do it with the railgun! You want to inflict only 1 reactor hole. When the enemy ship has one orange plume coming out of it, stop using the railgun, but keep them microwaved.
After less than a minute the enemy ship should run out of fuel and the lights will go out. If you shoot them too much they will go critical instead. Once they have gone dark, recover them with the manipulator arm.
If your ship doesn't have diagonal RCS, you will probably want to turn off your forward thrusters. Just grab the disabled ship and bring it home to the Enceladus.
If you are having troubles keeping a hold on the disabled ships, see Beginner's Guide to Derelicts.