Quote Originally Posted by кори
I am a little puzzled about the verb "учить", though. I was wondering why I would use "Я учу..." instead of "Я учусь...".

I am not good in terms this is why won't be able to explain with the help of right terms, however, I will try to explain the issue by means of illustrative example

Я учу + something - Я учу язык. Я учу правила. However, it can also mean that you teach someone, still this can be only possible if a pronoun (or a name) goes after учу - Я учу его (him) русскому.

Я учусь - means You are teaching something to yourself, so to speak. Я учусь Английскому. Я учусь вождение. It may sound like you are teaching yourself to speak English or to drive.

Compare

Я учу английский (correct) = Я учусь английскому. (Correct but very rare to be heard)
Я учу вождение. = Я учусь водить.
Attention
Я учу водить means You are teaching soeone to drive.