How do you say your grade in Japanese?

I assume this means 1st grade, 2nd grade, junior, senior, and so on.

You say what level of school you're in (elementary, middle, high, college, etc.) and then your year within that. For example, if you are a junior in college, that is the third level within college, so you'd say　大学一年生 （in hiragana, ãã„がくいちねんせい, in romaji - daigaku ichinensei). Just keep in mind that the years in school are different in Japan than in other places. For instance, there are only three years in high school instead of four.