For the 360, you will have to open it up. Essentially, you will need to flash a new firmware on the 360 DVD drive so that it will recognize burnt DVDs.
The PSP is different. There is a software hack for it. Basically, you can use a game to trigger a software hack which will allow you to downgrade the formware to a version which allows you to run copies of games off the memory stick.
There are great tutorials here on FST in the guides/tutorial section. You should check them out.
In addition, try these links.
http://360mods.net/Forums/viewtopic/t=142.html
http://www.evilpsp.com/forum/index.php?sid=47692b52
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