Let’s assume your original movie is called Orig.mov. Make a copy of the movie in the Finder; for this tutorial we'll call it OrigConformFrameRate.mov.
Start Cinema Tools (which comes with Final Cut Studio, and is located in your Applications folder). If you haven't created a database before, simply select Create New Database and then hit Continue. Select "File->Open Clip..." Open the copy of the movie (OrigConformFrameRate.mov) and after it is opened, click on the "Conform.." button in the window where the movie is displayed. Change the frame rate to the desired frame rate. Then hit the "Conform" button after changing the frame rate. You may now exit Cinema Tools. What we have done will cause the copy of the movie to play each frame of the original movie at the new frame rate, making it longer or shorter. This will also make the audio longer or shorter, which is why we are changing the frame rate on a copy of the movie, so we can use the original audio within FCP that is within the original movie.
Open FCP, and include both Orig.mov and OrigConformFrameRate.mov into your project bin. Create a new sequence (we’ll call it Interim Sequence), and drop OrigConformFrameRate.mov into it. When asked to "change sequence settings to match the clip settings?", answer "Yes". If you look at the Interim Sequence’s sequence settings, you'll see that the frame rate is set to the new frame rate we are converting to. You can get to the sequence settings by right-clicking (or option-clicking if you have a one button mouse) on the Interim Sequence in the bin, then selecting Settings... when the popup menu comes up, then hit the General tab.
Because conforming the frame rate in Cinema Tools may have made the original movie shorter due to playing each frame from the original movie at a different rate, place a copy or two more onto the timeline. This will make sure this Interim Sequence has a duration at least as long as the original sequence before conforming. As you may recall, this is exactly the pre-step process we perform when performing a slow down of clips with Twixtor.
Now create a new sequence called Final Sequence and drop the Interim Sequence onto it’s timeline. Apply Twixtor to the Interim Sequence within the Final Sequence timeline. Now here's the trick: set Twixtor’s Speed% to 100*(old frame rate)/(new frame rate). For example, if you are converting from 29.97fps to 24 fps, use a speed percentage of 124.875, which is 100* (29.97 / 24.0). Important Note: even though FCP often marks footage as 23.98, it really has a frame rate of 23.976. SO if you are converting 29.97 progressive to 23.98 progressive, use the speed change of 100*(29.97/23.976) or 125% , and NOT 100*(29.97/23.98) or 124.979
Now you may have noticed that the audio from the OrigConformFrameRate.mov has been slowed down or sped up, which is not what is desired. So in the Final Sequence, replace the audio with the audio from Orig.mov, which the original audio without any slow down or speed that the conforming process introduced. It is at this point you'll want to trim Interim Sequence within the Final Sequence"s timeline to be the same duration as the audio from the Orig.mov (this is where FCP"s snap feature comes in hande!), otherwise you may see the original clip repeat itself within the Final Sequence.
That's it!