From: Ol' Blighty
Welcome to the forums and to Distant Worlds Atreidi!
You can find abandoned ships that are either just abandoned, or are wrecks. If you find an abandoned ship that is not wrecked, just fly a ship up to it to claim it. If you find a wreck, you will need to send a construction ship to repair it.
When the repair is taking place, you will get a small research bonus that represents your crew repairing the advanced technology.
Once the ship is almost repaired, your empire should claim it.
Once an abandoned ship or an abadoned wreck has been claimed you can either a)Use it to fight, add it to a fleet or whatever, taking direct advantage of the technology, or you can b)right-click and tell it to retire at your nearest spaceyard. It will move to your spaceport and 'deconstruct' itself there (it is not instant) and when that finishes you will get a boost in a technology on the tech tree (partly research it). If the ship was very advanced you may even get such a boost you research the tech entirely! If you are the conquering type proably best to keep them and use them, if you are the peaceful type the tech bonus from retiring them will probably suit you more!
"My body may be confined to this chair, but my mind is free to explore the universe" - Stephen Hawking