How would I say, "I have been studying Korean since July?"
I think it's something like... 한국어를 7월부토 공부 했어요. Corrections would be appreciated but please keep it simple! I'm just a beginner.

Question

Answer

You are almost correct.

한국어를 7월부터 공부했어요. 
Or 
7월부터 한국어를 공부했어요.

Answer

First, you need to know the Korean grammar strucutres. Have been ~ ing: 계속 ~ 하고 있다. So, I have been studying Korean means 나는 한국어를 계속 공부하고 있어요. Since  means ~ 이래로( or 부터, 이후로 ,,)
Therefore, when you combine this whole sentence, you can say like this: 나는( 저는)  7월 이래로 한국어를 계속 공부하고 있어요.
Please see the meaning about since from a naver dictionary( we use it a lot)
http://endic.naver.com/enkrEntry.nhn?sLn=en&entryId=5c8748bc6cd749ddbd31bda00bbebd1a&query=since

Answer

7월부터 한국어를 공부하고 있어요 (just additional explanation^^)

Answer

두가지 표현다 좋습니다.
두가지 다 실제 사용되는 표현입니다.

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