Update: You might wanna try using Impalers PSX eboot creator tool which is a lot easier to use, you can check it out here! =)
First, download and install these two:
To begin converting PSone games to PSP you must first extract the ISO to your PC.
Insert the CD of your PSX game into your PC. In IsoBuster you will see the the session(s), track(s) and file-systems of your disc.
Right-click the CD listing at the top of the tree on the left and choose Extract CD RAW (*.bin, *.iso). It will ask where to save the BIN and after the extraction where to save the CUE.
For the BIN file to work with PSX2PSP you must add .iso to the end of the generic BIN file that IsoBuster created.
In Theme Mode of PSX2PSP open the Convert Menu. Under ISO/PBP File navigate to where you saved your ISO. PSX2PSP should automatically fill in the Game and Save titles and IDs.
(NOTE: If you are converting a multi-disc game make sure you use the same Save ID on each discs EBOOT.)
Under Output PBP folder navigate to where you want your EBOOT.PBP to be saved after conversion.
From here if you do not wish to customize the EBOOT.PBP menu you can click the Convert button and your playable EBOOT will be created.
If you do wish to customize your menu open the Customize PBP Menu.
Here you can choose which graphics are used for the icon and menu, more specific information will be added for this later.
After you have chosen the graphics you wish to use for your converted PSone game close the Customize PBP Menu and hit the Convert button on the Convert Menu.
Now copy your completed game folder to your PSP memory stick under X:PSPGame
You are now able to play your favorite PSone game on your PSP!
Not every game plays with 100% accuracy, tweaks and PopStation improvements come as sony introduces firmware updates for POPS. But how ever you can always use DAX, POPSloader to emulate which games run better on which firmware.
Not all psOne games plays perfectly on the PSP, some games work better on a certain firmware like 3.80 and some games may not but will work on another firmware like 3.90.. Thus you will need POPSLOADER it emulates other firmwares when you play psOne games on your PSP (ex. if you got currently have 3.90 and the game you want to play only works on 3.80, this add-on will let you play the game as if you are on 3.80 firmware). You can check out the giude in Installing POPSLOADERS here.(Originally posted here by Victoria)
Additional notes: i got this guide from somewhere else, credits go to the original.