My first-gen PSP (1000) can't do it, but if I'm not mistaken the ability was added to the PSP 2000 and PSP 3000 that followed - dunno if "you just used a cable" or if there were other hoops you had to jump through.
What I can tell you is that it was possible, up to a point, on the PSP 1000 as well, if you had hacked - or, as is known nowadays, "jailbroken" - it. There was a proggy, called "remotejoy" or something along those lines, that allowed you to "stream" your PSP's screen to your PC, in almost exactly the same way as if you were running some version of Remote Desktop, Splashtop or VNC on it. You had to use your PC as an "intermediate", though.
The "modern" way to do it is, as was mentioned, with no PSP at all, by playing the games straight through a PS TV. And there's also support on jailbroken PS3s for almost all PSP games, so that's another way to get them to the big screen, but it's hard finding a jailbroken PS3 cheap-ish these days - and I don't think it's worth it just for playing some old PSP games.