You need to have Custom Firmware. The most important thing needed, is what model PSP do you have and what firmware level are you running? (ie, PSP 1000, 2000, or 3000. Official Firmware 6.20, etc.)
You will need a Pandora (TOOL) Battery. And a program to make a "Magic Memory Stick". I like this program: http://pspslimhacks.com/psp-grader-v008/ I purchased my TOOL Battery here: http://www.dealextreme.com/details.dx/sku.12472 You'll just create the memory stick using the program, then use the TOOL battery to boot up your PSP into recovery mode and install the custom firmware from your "magic memory stick". The PSPGrader program has a little step by step instruction list. It's not that hard to do, and doesn't cost much.
It just flashes the programs you need to put Custom Firmware on your PSP. You can use any memory stick really. It just puts files on there.
The program installs files on the memory card that are required to install the custom firmware. So you will need to format your memory stick, use the program to install the custom firmware files, then use this new "magic memory stick" to install custom firmware on your PSP by booting it into Recovery Mode using the TOOL Battery. (Magic Memory Stick just a term used by the psp modders, nothing magic about it)
It's quite risky, but yes, you can make a pandora battery out of your own. Though some of the newer batteries are "Pandora Proof".
You COULD mod the current battery, but the risk of an exploading batter is a risk... I heard about soft modding psp batteries though, would anyone know if the 1000 could be done? As for the buying online part, ask your parents to do so, tell them you could potentially reduce the cost of buying games for the psp this way, if they want more reasons we could try listing them
It involves opening up your battery and cutting a circuit board trace on the inside. Once cut, it acts as a TOOL Battery. But a TOOL battery made like this cannot be used to power on your PSP, so you will be left with an unusable battery afterward. Unless you are handy at soldering. You can solder the trace back together and use it as a real battery again. But it's risky, if you accidentally touch the other traces with what ever cutting tool you are using, you may ruin your battery.
That's what Custom Firmware is, but you need to have a Pandora Battery in order to put Custom Firmware on your PSP.
You need a TOOL battery before you can use a hacked firmware though. Kind of a catch 22. You need a TOOL Battery to install Custom Firmware. You need Custom Firmware to create a TOOL Battery without using the hard mod method I mentioned. So your only option is to buy a TOOL Battery, hard mod yourself one, or find someone who has or can make a TOOL Battery for you.
But if you're using a Pandora Battery to flash your PSP, then you'll be able to run Homebrew. So using ChickHEN after the initial setup would be completely useless...