Follow the steps in this video, and you should be on your way to getting custom firmware (CFW) on your PSP 3000. This makes use of software called ChickHEN. You need to ensure that your PSP firmware is 5.03 or else this will not work!
This video goes step-by-step, from downloading the files to loading them onto your PSP.
Have an iPhone? Check out all 200+ new features coming in iOS 13.