First off, if you want your movie to sync properly, you will need to dump some files from an actual wii or gamecube. These files are copyrighted to nintendo, so you cannot legally download them. The easiest way to get them is with a soft modded wii, you can simply run a file (
here) and they'll magically appear on your SD card.
If you have a wii, but it's not modded, you can either mod it, or there are ways to do it without modding it. If you need help with that, just ask, and i'll explain. You can also do it from a hard modded gamecube. There should be instructions for that somewhere in that thread.
After that, you'll want to use the most recent version of the more-save-fixes branch, which you can find
here for the 64 bit version, which fixes basically all desync issues. The version available at the official dolphin site does NOT include this fix, so don't use that.
For settings, you'll want to turn dual core off (actually, the issue dual core caused may be fixed now, but i'm not sure. I'd keep it off just in case. It doesn't make a huge difference in performance anyway), and idle skipping off. And of course don't forget to change audio to dsp lle recompiler. You'll probably also want to set a hotkey for frame advance, and possibly change the save/load states to something that is comfortable for you.
Once everything is set up, highlight the game you want to play, then click emulation->start recording.