It can be a bit of a palaver getting the whole thing going. First, if you want to play over the internet, you need to set up a PSN account (if you don't already have one). Then, either way, you'll need the latest firmware for your machines, so do the update thing if you haven't already done so. Then, connect your PSP to your PS3 by USB cable and select 'Register Device' from the settings menu on your XMB. Once done, the two will be able to talk to each other.
Now, pop in a PSone disc (into the PS3 - stop trying to cram it into your PSP already!) and select Remote Play on both machines. If you want to use your home network, you don't need to sign into PSN - just connect to your access point and away you go. Otherwise, sign in and wait for the PSP to find the PS3, which can take up to 90 seconds.
Next, you need to sort out a connection quality setting that works for you. If you hit the Home button on the PSP, you can get into the settings option and decide whether you want a superior-quality video feed (better graphics) or better response time. If you're using a local network connection, you should be able to get away with having both of these up high. Try the presets if you're having difficulty and see what feels best to you. With firmware as it stands, the game won't fill the whole screen on the PSP - don't worry, it's not broken. This may well be improved with new firmware updates.
Above: You can set the PS3 to switch on and off remotely, but not all home routers allow it.
There are other options available from the PSP's Home menu, such as button settings - crucial for games that need all four PSone shoulder buttons (hint - assign them to the analogue nub instead). You should see an option that says 'PS Button'. This mimics the PS3's 'home' button to bring up the menu you would see if you were just playing the PS3, and not the PSP's home menu. So you can quit out and look at something else on your PS3, listen to music stored on it, or load a new game (if there's someone to switch discs for you).