It's a lot of fun to blog, but it can get old fast if no one is visiting! Getting your blog to the top of the search engines for your main key phrases should be your goal to make this traffic happen. Keep in mind that it will take time, but it's very possible.
You're going to need to learn about Search Engine Optimization to make this a reality. The very basics of this is knowing which keywords to focus on. These are what people are searching for in the search engines, and how they might find your blog. Some of these keywords get a lot more searches than others get, so it's in your best interest to eventually choose the ones that do get searched for often. Keep in mind that these are often more competitive than ones that are searched for less — but you might get lucky.
You need to focus your efforts on these keywords for now. Choose a big one that will take longer to reach, as well as three to four additional terms you're going to try and rank for. These should all be similar! Then, you're going to include these keywords in each blog post you make in various combinations. Always focus your posts on one term, and include the others only if they make sense. As you focus on these similar keywords the search engines will start to rank you more highly because your blog is tightly focused and relevant to what you're targeting.
It's not always that easy, however. A lot of ranking decisions are based on how many backlinks you have coming into your website. You need to do what you can to get relevant links that point to your homepage and your individual posts. You can get these links by writing articles to submit to directories, writing guest blog posts on other high traffic blogs, using social networking sites, using social bookmarking sites, and buying links (be very careful with this tactic.)
One of the best ways to get your blog to the top of the search engines is to show consistent, relevant postings over time. Google seems to favor domains that have had some time to age and that are going to be a good bet for their visitors. Remember — Google's (and other engine's) goal is to provide the best experience possible for the people who search with them. If your blog is going to be a good match for your search terms it will be easier for you to rank and stay there.
Finally, you need to make sure that you're always posting amazing content. The better your content and the more interesting your blog, the more people will link to it. There is nothing better than getting free links just because people liked what you have to say! Keep your mind on the SEO side of things, but also remember that you are ultimately catering to the needs of the people in your niche. If they like you, the search engines will like you.