Some activities that can help improve your writing are reviewing fundamental grammar concepts, reading a variety of work by other authors, and writing often. Some other things that can help include joining a workshop, and not being afraid to edit out much of what you write.
Even the most talented storyteller must become adept at language fundamentals in order to become a successful writer. If you're not very well-versed in spelling, grammar and sentence structure, then consider taking a class or reading books such as Strunk and White's "Elements of Style." One of the best ways to improve your own writing is to read the work of other writers. Pay attention to details like word choice, how dialogue is used and overall flow. Like anything, practice makes you better at writing. Spend some time writing about anything every day to hone your skills and develop your own style.
Joining a writing workshop, whether it's an informal coffee shop meet-up or a college class, can go far in helping to improve your writing. Getting honest feedback from group members can help you to take a more honest assessment of your work. When it's time to create a final draft, edit yourself relentlessly. Try to say things as concisely as possible, unless description or elaboration really add something valuable to the piece.