You log on to the PlayStation Store and then you go to the Welcome back and click that After you click free game one and then pick your game you go to free game two and pick that. Sometimes it does not show both games, but it should still be up where they say my downloads where the search is at the top of the page. I had to go there to find Dead Nation, since I already owned Infamous and LittleBigPlanet i chose that and Wipeout HD. I also had to make sure my console would not shut off on it's own. Maybe just for my peace of mind and changed the auto shutoff to 5 hours. The download process can be monitored by leaving the PlayStation Store and once the download has been completed you go to games and click on them because you are not done yet. They will need updates and the updates do not let you do other things while they download in the background.
Don't forget to join the PlayStation Plus network,You sign up for that after the same welcome back screen as the games. It expires 30 days after you join and there are free games there to download also, but remain yours to play only as long as you are a PlayStation plus member. There are PSP free downloads that I was not able to get, Maybe because I had never signed in a PSP
Some PlayStation games are free to download and are called demos
You need a PSN account before you can download games from the PSN.
No, you don't need to use a computer. You can connect the PSP straight to the PSN, and download games directly.
The PSN is the best place. There are no viruses for PSP, especially not on the PSN.
You can't run unsigned code on a PSVita, that means you need to download games from the PSN.
Yes, the PSP 3000 has a PSN icon on the XMB. From there it can access the PSN, to purchase and download games.
Not from the browser, no. You'd need to make a PSN account, then you can download demos and such from there, and if there's any games available for free, you can get them there also.
on the PSN store
You can look on the PSN for the latest games.
Yes, games can be purchased and downloaded from the PSN.
There is no way to download free PS3 games. The only exception to this is some small PSN games can be downloaded for free IF you have PlayStation Plus. Any site which claims free PS3 game downloads is either a scam or a pirate site (illegal).
You might be able to use the PC to buy the games from the PSN, but ultimately you'll still need to connect your PSP itself to the PSN to do the download.