In addition to reading (as suggested by others), practice writing in contexts that are already available to you. (Starting a blog is good too, but if you can't build a reader base that can be discouraging.) You're a CS major; that presumably means you are designing and implementing software. There is more to software documentation than inline comments in the code; go beyond that, even if it's not part of the assigned work, and you will both practice writing and develop skills that will help you in a software career. A lot of programmers can't write a coherent design document or technical specification; if you can, you're a step ahead.
Practicing writing is good, but how do you know how well you're doing? If your professors aren't able/willing to review documentation as part of grading your code homework/projects, see if your university has advisors who can help with that. Some schools have people whose job includes helping students improve their writing; usually (from what I understand) this means graduate students working on theses, but ask your curriculum advisor, any professor, or someone in the careers center if your school has such services. If it does, any of those should be able to connect you.
Finally, if your school has classes in technical writing (which will probably be offered by the English department), see if there's a low-level course that's open to non-majors. Such a class is likely to focus less on "literary" writing and more on explanatory "nuts and bolts", which might be an easier introduction than, say, a creative-writing class.