This is not a simple question, but I'll try to cover it...
There are two different ways to get free games on your psp.
1. Go to the Official Sony website here, and download (through your psp is easiest, but I think you can do so with your pc as well, but don't quote me) the demos they make available to you (after you make an account, that is). This will allow you to play demo versions of several games, but not nearly so many as there should be. (my opinion, there) This method is the fully legal way.
2. Hack (or have someone else hack) your PSP. (this is not a simple process without someone that already has a hacked psp, so I'm not going to go into details here. If you want to pursue this line, google 'how to downgrade my psp', and you should find a wealth of information, but you will have to dig to get to the info you need) Install custom firmware, like 3.90m-33 or higher. Download a torrent client (like uTorrent, or BitTornado or the like). Install the client on your pc. Google (or other search engine) 'psp game torrent'. You should find a BUNCH of them available. Download one of the bundle torrents, and tell your pc to use your new torrent server to access the file. This should launch the server, and ask you which files you want to download (if not, you need to change some settings so it will. Check with the source site to find instructions on how to set this up). Click 'uncheck all' (at least in uTorrent that's what it is), then go through the list and pick the games you want. If you want them all, and have the drive space to download them all (it will probably be a LOT of data), then don't uncheck any of them, or just the ones you DON'T want. ...Then you wait...probably for a long while... (there are some places where you can direct download files for games without using torrents, but they're usually pretty hard to find, torrents are easier) When you have at least one of the games downloaded, connect your psp to your pc, and copy that file to the folder called 'ISO' (this is after you have uncompressed the file if it downloaded as a .zip or other compressed file). The file will probably have the extension .iso or .cso. If there is no 'ISO' folder on your psp's memory stick, just make one, but make sure the name is in ALL CAPS, or the psp won't recognize it. Then disconnect from the pc, scroll over to the game icon on the psp's menu, scroll to the bottom icon (memory stick) and press 'X' you should see the game you copied to your psp. If there are problems playing it, you most likely have some settings that need to be changed. You got some learning to do, so hopefully you will have at least tried to learn how to make changes in your now hacked psp. (btw: This way is COMPLETELY illegal, and harms the handheld gaming industry by not putting money into development of games, but it's possible, and you DID ask, so I'm tellin you.)
Hope this has helped in some small way, and you have a great day.
There are two different ways to get free games on your psp.
1. Go to the Official Sony website here, and download (through your psp is easiest, but I think you can do so with your pc as well, but don't quote me) the demos they make available to you (after you make an account, that is). This will allow you to play demo versions of several games, but not nearly so many as there should be. (my opinion, there) This method is the fully legal way.
2. Hack (or have someone else hack) your PSP. (this is not a simple process without someone that already has a hacked psp, so I'm not going to go into details here. If you want to pursue this line, google 'how to downgrade my psp', and you should find a wealth of information, but you will have to dig to get to the info you need) Install custom firmware, like 3.90m-33 or higher. Download a torrent client (like uTorrent, or BitTornado or the like). Install the client on your pc. Google (or other search engine) 'psp game torrent'. You should find a BUNCH of them available. Download one of the bundle torrents, and tell your pc to use your new torrent server to access the file. This should launch the server, and ask you which files you want to download (if not, you need to change some settings so it will. Check with the source site to find instructions on how to set this up). Click 'uncheck all' (at least in uTorrent that's what it is), then go through the list and pick the games you want. If you want them all, and have the drive space to download them all (it will probably be a LOT of data), then don't uncheck any of them, or just the ones you DON'T want. ...Then you wait...probably for a long while... (there are some places where you can direct download files for games without using torrents, but they're usually pretty hard to find, torrents are easier) When you have at least one of the games downloaded, connect your psp to your pc, and copy that file to the folder called 'ISO' (this is after you have uncompressed the file if it downloaded as a .zip or other compressed file). The file will probably have the extension .iso or .cso. If there is no 'ISO' folder on your psp's memory stick, just make one, but make sure the name is in ALL CAPS, or the psp won't recognize it. Then disconnect from the pc, scroll over to the game icon on the psp's menu, scroll to the bottom icon (memory stick) and press 'X' you should see the game you copied to your psp. If there are problems playing it, you most likely have some settings that need to be changed. You got some learning to do, so hopefully you will have at least tried to learn how to make changes in your now hacked psp. (btw: This way is COMPLETELY illegal, and harms the handheld gaming industry by not putting money into development of games, but it's possible, and you DID ask, so I'm tellin you.)
Hope this has helped in some small way, and you have a great day.