There are a couple of ways to deinterlace. One’s cheap and fast, and one’s expensive, better, and slow.
You can use FCP’s Deinterlace filter. It does what a LOT of cheap and fast techniques do: it duplicates the pixels from one field to the other field. Hey, doesn’t that mean that you lose half the vertical resolution? Well, yeah, but astoundingly, the results look pretty darned good!
You can use third-party plugins to do the job, too, and they tend to be pricey. One that comes to mind is Magic Bullet Suite; there are others, too, and they all do other tasks in addition to deinterlacing.
This kind of software works on the fact that the fields in interlaced video are offset temporally. In NTSC, the second field is scanned about 1/60 of a second later than the first field; in PAL, the figure is 1/50 second. The plugin’s task: create two fields that look like they were scanned at the same time… which is what happens in progressive-scan cameras. So it looks at the pixels from both fields, algorithically splits the temporal difference between them and creates an entirely new frame of two fields, unified in time.
Needless to say, this kind of deinterlacing takes a little bit of processor time, and there are several different algorithims for your individual circimstance… so you may not get it right on the first try.