There are a couple options.
1) The best option IMO would be to use the component/composite out on the PSP to a capture card. This works with all games and has basically no input lag, but does require you to own a capture card and the AV cable for the PSP.
2) Alternatively, you could use Remotejoy to stream the PSP's screen over to a PC. This unfortunately does have input lag, can cause performance issues in some games, and doesn't work with every game. This option is basically only good if you have no money and don't want to buy a capture card + AV cables.
And then you could always just emulate the PSP instead of playing on the actual console, but you'll need a half decent PC for that.