I am interested in Sociobiology. Which academic field should I study?
What fields are sociobiology and evolutionary psychology?

Sociobiology (aka. social evolution) is a subfield of evolutionary biology. 

Evolutionary psychology is a subfield of both evolutionary biology and psychology. Evolutionary psychology is, for the moment, very theoretical without much (if any) empirical testing. For this reason, not only natural scientists 
 and social scientists work on the subject but some philosophers have also contributed (such as Daniel Dennett for example).

How to become a researcher in one of these fields?

Biology.SE is not BiologyCareerAdvice.SE. We have way too few information about you to give reliable career advice anyway. Also, I am not trained in any way to give you carrer advice.

That being said, a priori, start with a Bachelor in Biology and follow up with a master in Evolutionary Biology. Because evolutionary psychology is very inter disciplinary, I would personally advice to go with whatever broad field of study attracts you most. If you are more into psychology than biology, please go with psychology. If you are more into philosophy than biology, then go into philosophy.

Short intro to evolutionary biology

For a very short intro course to evolutionary biology, you can have a look at evo101 by UC Berkeley.