This won't void your warranty or brick your psp this question has been asked multiple times...Before i even put it on the web i had multiple people test it just to be on the safe side,I also test each version on my psp before releasing it as well so you can enjoy it worry free so please do so.
1.Download your selected version of the game all versions are compatible with all psp's so just get whichever one you want or even all of them at once its up to you.
2.Use a program like Winzip,7-zip,Winrar,ect. And extract the file to a location of your choice.
3.After you do that there should now be a folder titled lamecraft or somthing along those lines depending on which one you downloaded.
4.Then you just connect your psp to the computer via usb cord. Copy the lamecraft file and paste it in your Psp game folder on your psp (yourdriveletter:\psp\game).
5.Now disconnect your psp from your computer and go to the game icon on your psp and there should now be a lamecraft icon there. Click on it and wait for it to load. (A black screen will show for about 15 seconds before the game starts dont worry its normal.)
6.Enjoy minecraft on your psp!
7.After you played for a while come on back to the site and let me know if you like it with a forum post.