You have a hard road ahead of you if you want to pursue the Shinto clergy as a calling. Shinto is a major interest of mine, in both scholarship and practice, and I, too, at one point considered seeking out a chance to be clergy. Here are some thoughts and ideas (as well as some of my big mistakes) for you to consider that might help you out.
-Check local resources first, especially if you're not in Japan. There happens to be a pair of Shinto shrines in North America. They have already been mentioned. Last time I looked, Rev. Barrish at Tsubaki Jinja of America needed an apprentice. Give him a shout and see what comes of it.
-Read, read, read, read, read. Then read some more. Get 'under the skin' of the concept of Shinto from an academic perspective first. This isn't to discourage you from practicing and learning from that, but you need to know the book facts as well.
-Japanese. You've got to know the language, written, read, and spoken. Not only is it very difficult to communicate without this skill in Japan, but all rituals and most scholarly and practical written works on the subject are in Japanese.
-Formal training. Two universities in Japan, Kokugakuin in Tokyo and Kogakkan in Ise, offer a 1-2 year course in Shinto priest ordination. You'd have a hell of a time getting in, but if you are 100% dedicated to this idea, it's at least worth exploring. This failing, hunt up a shrine that is willing to take you under its wing for an apprenticeship.
-No tattoos. This is where I made my only big mistake, I'd say, and it's what kept me from having a chance to apprentice. I got inked before I checked into the requirements, and I only found out later that in traditional lines of thought, tattooing is considered permanent kegare, or ritual impurity. I have heard many explanations as to why it's so frowned upon in Shinto circles (especially considering that the original Yamato people tattooed their faces and necks), and the best explanation I have heard is that tattooing has strong social connections to "bad" images in Japan--gangsters, criminals, etc. I'm sleeved beyond salvation these days and my life has taken me elsewhere, but if you have a small tattoo or two and are very serious, you can get it removed and still be able to pursue your studies.
Best of luck to you, though. Drive on in spite of what people may say, and you'll find your means.