Well, the simplest way is to basically share your channel and the videos to your followers as you upload them. Some prefer to link to the video directly which is displayed on the tweet, others used the video thumbnail with a link to the video in the text, usually a short version of the link, like a Bit.ly link to it. The thumbnail can often be more catchy than the video itself on the tweet.
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.
Also actually engage in conversations on Twitter. Not about your videos but just as you would in a party or when something the Minnesota situation hits. Forget the stupid promo. Actually get human and talk and share your views on something sensitive. Some how people will realize you're real and in it for more than just yourself, and start conversing and eventually watching, comment, subscribe to your videos as well as buy your products.