The absolute #1 thing you can do is get your bills paid BEFORE THE DUE DATE. On any bill you receive, the Due Date will be printed on it. This is NOT the same as the "penalty date" or the "we'll shut off your service" date, which are always AFTER the Due Date.
Many people have the money to pay their bills, and could easily pay them by the Due Date, but chose not to, either due to laziness, or because they don't take that date seriously, since visible penalties, such as late charges, or services being suspended, don't take place on that date, but they ARE harming their credit scores.
Paying off your credit cards with a zero balance is actually NOT especially good for improving your score. USING your credit, and paying the bills on time, is the best way to maintain a good score. Doing this on multiple lines of credit (car note, credit cards, cell phone company, etc.) looks even better, as long as you don't have too much outstanding credit compared to your income. Not counting a home mortgage, ideally you should have less credit than 1/3 of your gross yearly income, so if you make $60,000 a year gross, you don't want more than $20,000 in credit (used or not). That would mean, say, a $10,000 car note, plus 2 credit cards with $5,000 limits each, or something similar.
Another thing to remember is that what improves your credit score isn't ALWAYS what is best for YOU. Creditors are happy if you only make the minimum payment, because you'll be paying more interest to them over a longer period that way, but it's in YOUR best interest to pay things off much sooner if you can.
Always pay down the credit line with the highest interest rates first, even if it means making the minimum payment on the other bills. If you have an extra $200 a month you can put towards paying off credit, paying that to your home loan at 4.75% instead of that credit card at 15.9% means you are totally screwing yourself.