If you are playing the SP game, just shoot them with your guns. Some times it's best to use a less powerful gun so that you don't blow up the "loot" too! And remember that in some systems, many of the wrecks will already have been stripped of their guns and cargo. (You should hear a "rumour" about that at a base in the system.)

If you are in MP on line, then most likely somebody has beaten you to the wrecks and already got the goodies.

It is enough to shoot the wreck once, then some items will drop from it. Use your tractor beam (B by default) to pick them up. While playing online, when a player loots some wreck, no more items will drop from it for anyone. You have to wait for server restart to reset wreck loot. Consult your server's admins on how often does the server restart.

Ok they reset the server like every 10 hours. So I guess I just gotta wait untill the next reset. Thanks for your help guys, I was starting to think the server sucked.

Some wrecks don't blow up but you can still get the loot.