How can students improve their writing skills?

There are many strategies students can use to improve their writing skills. Which strategies will work depends to a degree on the individual student. A middle school student learning to compose paragraphs and a PhD student struggling to write a dissertation face different problems. Similarly, learning to write in a second language requires different skills than writing in one's native language.
The single thing proven to improve writing skills the most is reading. There is a very strong correlation between quantities of leisure reading and writing skill. Although any reading is better than no reading, the more sophisticated the vocabulary and syntax of what you read, the more you improve your writing. Reading a children's book, teen fantasy, or blogs is less effective in developing writing skills than reading more complex materials such as major novels, history, poetry, or other complex, adult-geared reading. 
Next, as with any skill, practice makes perfect. The more you write, the better you will write. Taking writing-intensive classes requiring regular essays develops your writing skills.
Finally, many universities have writing centers that offer students free individual tutoring.