Source : psp-hacks
You will need:
1. An hacked PSP (Phat or Slim) (Recommended 5.00 M33-6 FW)
2. An PC (to get the files)
3. An USB cable or an Memory Stick adapter
4. An Memory Stick (with at least 20 MB free (I don't have the exact MB # that PSPKVM and Opera Mini takes but I think that 20 MB should be enough))
5. An Internet connection (both on your PSP and in your PC)
6.You need a WiFi connection before running the app, then open PSPKVM, then connect and torun Opera.
First, get PSPKVM 0.5.1 app
Place in the folder X:/PSP/GAME5XX/ were X: is the letter of your drive (copy the ENTIRE pspkvm folder!).
Then, get the Opera Mini files here.
Choose your favourite Language, and download the two files.
Place them in the root of your Memory Stick (were you can see all the other folders).
You're almost done!
Now, unplug your PSP from your PC and go to the GAME menu on the PSP, and launch PSPKVM.
If you haven't set up an Internet connection, choose "Network Set-up" (remember, in this app ENTER is with O, not with X!).
Now, click on "Find Applications", and select the file "opera-mini-advanced.jad" (should be on the root). Press O and it should ask you if you want to install the app, click yes (the bottom options are with [Select] and [Start] if you haven't already figured it).
Choose the device J2ME 480*272 (this adjusts Opera to the PSP screen size).
Wait to it to finish.
Done!
If you did everything correctly, "Opera Mini" should be now on your main PSPKVM menu.
Click on it to start Opera Mini.
To change the settings...
Launch Opera Mini.
Go to Menu>Tools>Settings.
You can choose an custom color theme, font size (I recommend small), and more.
Have fun with it!