If you are currently on an older custom firmware (such a 5.x or 3.x) then you might just be able to run an official update and jump right to the hacking steps, but if the PSP gives an error when you try then you will need to flash-install a clean original firmware before you can upgrade to 6.20 or 6.60. This is done via Hellcat's Recovery Flasher and a copy of the original firmware to flash.
- Download Hellcat's Recovery Flasher, and add the RECOVERY folder to your PSP's GAME folder.
- Download the Official Firmware 5.00 firmware file (search google for this), rename EBOOT.PBP to 500.PBP, and stick it in the root of your memory stick.
- Run Hellcat's, and hold L+R+Select while it's loading. When it runs it may warn you if you have GAME plugins enabled, and it will disable them, simply run Hellcat's again.
- When it loads, confirm your choice to enter advanced mode.
- At the second (garbled) warning, Select I AGREE, now take me to the program!
- At the main menu, make sure that Target FW is on 5.00, then go down to /! Install clean ORIGINAL FW (DANGEROUS!!!)
When the process is done you should be on a clean version of 5.00. This will ensure that you can properly upgrade to the latest firmware you want to hack.
Taken straight from the sticky:
http://gbatemp.net/threads/how-to-softmod-hack-your-psp.293978/
Now, you have to reflash 5.00. I had 5.50 Prome-2 way back when on my 1000 model when I first got it, and the only way off of it was to reflash. By trying to officially update, you may have accidentally caused a partial brick. If you can still power on to boot Hellcat's Recovery Flasher though, do it. If you can't and you did brick, the only recovery is through a magic memory stick and a pandora battery, which, lucky for you, the 1000 model is compatible with. To note though, you do need a legit produo stick to create a magic memory stick, as fake cards and adapters won't be magicgate compatible (or at the least, they are highly unlikely to be).
I do hope you can just run the recovery flasher. It really is super simple and the easiest way to go. If you have to start playing with a pandora battery and such, it will just cost you money and more time all because you jumped the gun and did what basically all old CFW warned you never to ever do, which is why they faked the firmware number to begin with.
Edit: To note, if the recovery flasher is failing, odds are you really screwed something up. I'd suggest getting a pandora and a produo stick (a legit one), or just buying another PSP. Whichever is easier for you. All PSP models can be hacked to the exact same CFW at this point, so if you can find another model on the cheap, you may be best off going for it.