How to access Playstation network from an updated old psp?

I think that one of them is the Final Fantasy Aniversary Edition There are many dungeons in that game and there is Monster Hunter 2 for PSP Hope I helped
LOL, looking at all of these answers.
a few points to make:

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1)yes, you do need a pandora battery and a magic memory stick, here is a tutorial on how to make both, suggestion: buy a pandora battery instead of making one, some sites have it cheap.
Dont be afraid of bricking(breaking) your psp. You can downgrade it using a pandora battery and magic memorystick again if you do. HOWEVER, this does not mean you dont have to be careful, be cautious and follow directions carefully.

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once you have a pandora battery and magic memorystick, you're all set to go to downgrade it and then you can just place your games into an ISO folder on your memorystick. here is a tutorial on how to do that
Find someone that can hack your psp and install custom firmware. Some stores do that for a small fee. Don't try to install custom firmware yourself because any mistake you do can PERMANENTLY break your psp.
Download some iso or cso game files from the internet or buy them from stores. You can find the games you want using www.torrentz.com search engine or from psp homebrew sites.
After you've got the custom firmware and some games, put them on your PSP's GAME folder. You need a mini USB b-type cable which is very very common and you probably already have it.
Buy them at the store, and put the disc into your PSP. Asking how to steal games is against Yahoo's community guidelines.
I've just got a PSP 3000 which I bought three days ago.I've never had a PSP nor have I played any games on it.I have the PSP but i don't know which games would be the most fun.I need help finding games that are worth buying at this time.My interest is mostly action FPS or sports genres.

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Well, theres always the faithful Grand theft auto, both vice city stories and liberty city stories. For sports i reccomend
Good luck, and have fun