Final Cut has several file types, stored in different places:
1. First, there’s your Project file. This is the most important file- and in fact, if all the media in your project came from DV tapes or built-in elements like titles or color mattes, this is the only file you actually need to move to another computer.
If you move this file, and re-batch capture your clips, and rerender, you’ll back back to where you were on the other computer.
But usually you’ll want to bring other files with you. The next file type would be:
2. Your video files – these are your captured video and audio clips. These are usually stored in your Capture Scratch folder in a folder with your project name (unless you saved them elsewhere or moved them). If you move these to another computer, you should only have to reconnect one file, if you have the reconnect all files in this relative path option checked.
3. Other media/project files – you might have Motion or LiveType projects, Photoshop graphics, After Effects animations, or any number of other media files for your project- obviously you’ll want to move these over to the new system, and you might want the original project files also
4. Render files – there are exceptions, but my advice is to not move render files- this can lead to problems, it’s better to rerender on the new system. If you must move them, they are in the “Render Files” folder.