How do you download demo PSP games to your PSP?

You can purchase and download games from the PlayStation Network, accessed from the PSP's menu bar.

There's an option to connect to the playstation network, on the PSP's menu bar. Here you can purchase and download games.

You can download games from the PlayStation Store, but you cannot run homebrew unless your PSP is modified.

Yeah, just download them from the PlayStation Store. (You need internet access, though)

The PSP has a menu bar called the XMB, on the right hand side you can find the PSN icon. Connect to the PSN, and you can shop for games online. Once you've paid for a game, you download it from there...