Have you ever picked up a book or read an article and instinctively loathed or loved the writing style? What made that difference to you? It might sound simplistic, but the best way to learn to write is to do it. I'm mainly a fiction writer, but fiction and nonfiction writing both have a certain feel to them. A good starting place for both types of writing would be keeping a journal or a blog. Slight confession here, I'm terrible at keeping up with a blog. I'll start it all enthusiastically and then forget about it a week later. However, I do write a lot, especially in the summer.
Try some simple exercises. Take a common household object and describe it three different ways. Make up some fantastic tale about the object. The more details you inject into your sentences, the easier it will be for your reader to understand you. Give the object some personality. Make it come alive.
Example 1: nearly useless sentence
There was a blue pen.
Example 2: slightly better sentence
The blue pen sat on the corner of my keyboard.
Example 3: even better sentence
The baby blue Pilot pen stared back at me from the corner of my keyboard, daring me to pick her up and write something grand.