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.

Verpassen Sie nicht die Gelegenheit, bequem von zu Hause aus eine Sprache zu lernen. Stöbern Sie in unserer Auswahl an erfahrenen Sprachlehrern und melden Sie sich jetzt zu Ihrer ersten Unterrichtsstunde an!