There may be no one best way to jumpstart the usage of a hashtag, but there are several things you can do. The first is to make sure you are using a hashtag that has not been targeted as spam by the social media programs on which you wish the hashtag to appear. A tool like Hashtags.org may be a quick way to help you check on all the various platforms.
The second thing to do is to create entertaining and educational material. You want your audience to continue to read your tweets and not get bored. You may want to consider sending at least three tweets a day in the beginning.