Playing psone games is easy.
You need to either download the PSX eboot or make it yourself. I download the eboot and have never made one, so I couldnt tell you how to do that.
When it comes to playing them, you made need popsloader, this allows you to use different custom firmwares loaders in order to load the psx eboot.
It is illegal to ask for the pops because they are derived from the "official" sony firmware somehow. You can easily find these by googling "popsloader 380v2" as this is the newest set.
you would then follow the guide on how to use pops... simply place the "seplugins" folder on the root of your card, then as you boot up your psp, hold "R".
This will bring u to the PSP recovery menu, select "plugins" then enable pops.
Place the PSX eboot in the PSP/Game folder.
As you select the PSX eboot fo the first time, you can select which pop you want to load it with. You can also change pops by holding "R" as you select the game. There are guides that will tell you the best pops to use for each game.
have fun, hope this helps.