Halmos's article contains a lot of good advice at the tactical level, the writing equivalent of "face your audience". This is stuff you have to get straight: if your notation is crazy then your potential readership is already zero. Fortunately this is largely a matter of acquiring good habits.
Next, you have to constantly keep your reader in mind. Whenever you are faced with a choice, ask "What would be best for my reader(s)?" It can be useful to assign someone you know well to this role, because it makes it easier to stay consistent. Remember that it is much more important to be clear than it is to be complete. Be prepared to do a lot of rewriting.
If you follow these suggestions, you will with practice become a competent writer. To become a good writer is much more difficult. Writing good mathematics is no easier, and no harder, than writing good prose on other topics. Read a lot, find good examples that you like and think carefully about why they work.