Brevity, it's said, is the soul of wit. Hemingway once wrote a six-word short story: "For Sale: Baby shoes, never used." Try writing your own story using only six words. A popular variation on this is the six-word memoir, in which you catalog events from your life in six-word blurbs. Also try descriptions, action sequences, expositions and climaxes, all in six words exactly.
Choose five to 10 words at random from the dictionary. Now, write a 200 word story that uses all of the words you chose. Another variation on this is to have someone write a first and last sentence for you, leaving you to fill in the middle. Focus less on eloquence and more on an engaging plot.
Like muscles, writing skills need to be exercised daily to stay strong. An easy way to do this is to write for 10 minutes every day as soon as you wake up or right before you go to bed. The times before and after sleeping are ripe for creativity, as your brain is in a hypnagogic state, where it makes connections it otherwise would not.
Pick a song from the radio or a photograph from the newspaper. Your task is to write the story that goes with it. Do not tell the story the song or image tells, but rather write a story based on the feeling and atmosphere that your inspirational object provides.
As you go throughout your day, create a mental "play-by-play," narrating the events going on around you, including dialog. For an added layer of unreality, use a third-person omniscient narrator that knows the thoughts of everyone, including yourself. This allows you to try and figure out what a stranger's life is like, which can be an exercise in its own right. Most importantly, look around you. Narratives are happening every second of every day; you just have to learn to see them.
No one talks like a book, but your reader should feel like the book is talking to them. This means that your dialogue must be sufficiently natural to sound human, but not so human as to involve the clumsiness and constant repetition and errors that occur in everyday speech. Go to a public place with a notebook and write down, as best you can, two or three conversations, word for word. Then go home and edit the conversations down to what would be a version more appropriate for a novel, creating the impression of normal speech without actually taking dictation.
If it has words on it, read it. When you see something you particularly like, write it down. Learn from both what you enjoy and what you hate, be it an ad at a bus stop or "Moby Dick." Even if you don't find anything to take note of, keep reading. The more you read, the more your brain becomes familiar with the process of writing and you will unconsciously improve your skills.