Direct to the PSP via the Internet
If you can connect to a wireless Internet connection using your PSP console, you can download games from there. All you have to do is log in to the PlayStation Online Store, purchase the game and start your download. It takes awhile for the game to download and install depending on your connection, but this is the most direct way to download games to your handheld.
Using your PlayStation 3
You may also use your PlayStation 3 to download PSP games in a manner similar to the way you would on your PSP. All you have to do is download the game to your PS3 and transfer the file to your PSP using the USB cable included with your console. This process seems to work quickly and is efficient.
Remote Play
Another option is to stream games to your PSP using Remote Play. Remote Play allows you to play certain games on your PSP while they run on your PlayStation 3. This connection works wirelessly, and while it does not actually download the game to your PSP, it does allow you to play them from your PSP, using an Internet connection. This can be set up using by selecting the Remote Play option on the PS3's XMB.