You'll need a pandora's battery, they sell them on ebay.
You get a memory card and batt, plug them both in and press X then when it resets your running 3.71 m-33.
3.40oe-3.80m33 Custom Firmware Installation Guide. VERY NOOB friendly - PSPMod.com - Sony PSP Mod & Hacks Forums
There are links to downgrading here to, but for the slim you really need the battery.
Dark-AleX - PSP Developer
Latest firmware.
If your unsure you can buy the PSPs already done or the batteries off ebay.