Gizmodo has a detailed walkthrough that guides you through the process of getting homebrew apps running on the PSP Slim (or any PSP, really). They skip the whole step of enabling service mode on your battery, since there are some cheap service mode batteries available for $25 that will save you the effort.

When you’ve completed the walkthrough, you’ll have the latest hacked firmware installed which will allow you to run homebrew apps designed for the PSP, as well as any old PS1 games that you own and care to rip.

How To Hack Your PSP Slim For Homebrew Apps