Research hashtags on Twitter that relate to your video. Try not to dump a bunch of hashtags into your tweet though.
What I usually do is make a small clip of the video, instead of having a thumbnail.
It actually seems more and more that hashtags are irrelevant on Twitter seems that when you search, results even with no hashtags will show up under trending.
I think think the best way... but I don't have that much experience with twitter, is to use your profile as a funnel, your tweets occasionally, and I've heard it's like a 1/10 rule or something along those lines. 1 out of 10 tweets should be a promotional video, then the other 9 tweets should be spent building a community, discussion and conversing with other people's tweets for a NON promotional means.
If all anyone does is just promote, promote, promote, no one is going to be interested in your channel or your twitter.