DO strive to learn to type as fast as you can handwrite.
DO focus on using all 10 fingers.
DO pay attention to spelling. Typing practice can help you with your spelling.
DO practice regularly. Go for frequent short practices -- preferably every day. Your brain learns better that way.
DO use the keyboard for writing. Applying your practice to real writing is the best way to learn.
DON'T worry if you look at the keys when you type. You are learning to compose, not copy.