배우다 is the dictionary form and cannot be used on its own, so you need to find it's stem, which is... 배우. You then add + 고 있어요 which is the present continuous tense. 저는 한국말을 배우고 있어요 I am (busy/currently etc) learning Korean. 저는 한국말을 배워요 is also correct. In these cases ,를 is an object marker. This means you are doing something to the object (한국말 )and to specify this you have to add the marker 를. 한국말 한국어 these are interchangeable and mean the same thing ^^