Asking Someone How Their Chinese Studies Are Going
It's correct. It sounds native enough. 
"怎么样" in this sentence is used for asking how the things are. i.e. Are they good or bad? It's the same in "你过得怎么样" (literally "How are you getting along (these days)? ")
Your friend could answer "还行" ("not so bad") "很好" ("very well") or "不怎么顺利" ("not so well"), as a few examples.