What you will need: PSPKVM, Opera Mini files, a wifi connection.
Once you have played the PSPKVM and Opera Mini files onto your PSP, launch PSPKVM and locate your Opera Mini files. Open them with O and it will install them as an application onto your main menu. Now that it is installed, DON'T LAUNCH IT YET! It wont work. First, go down to Network Setup and make sure you are connected to your network. Now go down to Opera Mini, but first hit Start. Go to select preferred device, and hit O. Make sure that J2ME Standard(480*272) is selected. Hit start again to save. Now press O to launch Opera Mini. The bottom left option is declared by Select, and the bottom right option is declared by Start if you haven't figured this out already. If you can't figure out or can't get used to the typing options when trying to type in an address, I suggest you navigate to a site like google and click the text box, which will open up an easier typing box from the built in emulator.