The simple answer is that for the most part, your religion has little meaning in Japan. You will be treated the same as any other foreigner. Japan isn't the kind of place where different rules apply to different religions. The rules you generally have to be most aware of are firstly that politeness is valued very highly in Japan compared to other countries, and secondly that there is a role in that society for a foreigner that cannot speak Japanese, unlike in many other places. In America people are very intolerant and rude to people who can't speak English, but Japanese people are very polite to foreigners. However it may still help to memorize a few important phrases in case you have to interact with someone who doesn't know English.
If you want more details on the religion situation, I might be able to give you a little bit of information. In their beliefs, Japanese people are very secular; many believe in a God, but not in any particular religion. Culturally they are a mixture of Shinto (a Japanese variety of paganism), Buddhist, and Christian, and religious ceremonies do play a part in their lives. Specifically, marriages are usually Christian, they visit Shinto shrines from time to time, and funerals are usually Buddhist. They do not see any inconsistency in living this way.
While a couple relatives and I were visiting Tokyo last December, we went to look at a Shinto shrine called Meiji Jingu. While we were there some college students came up and told us "We're the English Speaking Club. Is it okay if we guide you around the shrine?" We said yes, and they showed us around. During the typical shrine visit in Japan, you wash your hands in water before entering the main area, and you go up to a place where there is a large donation box, where you throw a coin in and make a quick prayer to the local Shinto god, while clapping your hands twice. We did the ceremonial washing, because we figured it was just a matter of politeness and respect. But we would not make donations or do the prayer ceremony, or participate in any sort of fortune telling. We explained that it was because we were Christians, and our guides understood (specifically, we said "We can't do this" and they said "Are you Christians?", so it was clear they already had a grip on the situation). We also happened to see a Shinto wedding procession while we were there. It was pretty interesting.
I went to one Christian church service while I was in Japan. The church I visited was in western style, and the service was an English-speaking one. There were almost no traces of Japanese culture in the service; walking into the building felt like I was in a different country. This bothered me a little bit, because I feel like Christianity should be more integrated with the local culture, and I wondered if the non-Japanese might have been attending there to escape into their own culture they were comfortable with. I'm not sure though, I only went there once. At least the church was very multi-cultural among English-speaking people, and wasn't just full of white Americans.
If you want a historical perspective, you may want to talk to somebody who's more of a history buff. I do know that in the early days of Christianity in Japan, many of the working-class peasants were very excited about Christianity when missionaries came to teach it, but the government rejected it and very heavily persecuted Christians. In the end, Chrisitanity never really took root in Japan. There are many arguments about why this was the case, but I think it had something to do with the way that Christianity was tied together with western culture and, at least from the government's perspective, carried with it the threat of the western imperialism that ravaged many other cultures around the world.
So yeah, it's complicated. If you're planning on visiting just for the sake of visiting, you should be fine without any special training, but if you're visiting for the sake of religious activities, you may have a tough road ahead of you.