This is relatively easy but your PSP does need custom firmware. The type of java games are, well any but some work well and others don't. One main reason people do this is that you can run opera mini on your PSP using this.

Step 1: What Ya Will Be Usin'!

Hardware: A Psp ( custom firmware ONLY )
A PC
A PSP usb cable

Software: PSPKVM (http://www.pspkvm.com/(Click On Downloads)
Optional: Java Games (http://www.getjar.com/software/Sony-Ericsson/W850i)
Opera Mini (http://www.getjar.com/products/3334/OperaMiniWebbrowser)

Get these things before you continue...

Step 2: Install PSPKVM

Copy "PSPKVM" to /PSP/GAME or /PSP/GAME150 or /PSP/GAME5XX folder.

Depending on what firmware you have or just try each of them and see if they work.

Heres A Video: http://tinypic.com/player.php?v=2vcj9s2&s=5

Step 3: Using PSPKVM!

Put The java games in a folder of your PSP ( like: Java Games + Apps )!

Then:

Run PSPKVM on your PSP
Click Find Applications (By Pressing Start)
Then Click Install from memory stick ( by pressing start )
Then Go into whatever folder your java files are in ( press O )
Then press your java game/app ( by pressing start )
Then click J2ME standard (480*272) ( by pressing O )

Step 4: Before You Try to Use Anything!

Exit The Application ( if you are on one ) and :

1-Start PSPVKM
2-Go to network set up. Press start to launch
3- click your network name. Press start
4- wait for it to finish and click done. Press start
5-Press Select to go back to the main page
6- Start opera mini!

Note : Your network needs to be configured on your PSP before you do it.