Learn what your project is actually going to cost. Don't get just one estimate. It is not necessary to get more than 5 estimates. 3 is usually ideal number of Estimates.
Ask to see some of your contractors work. Also ask to see pictures of their work. Ask to talk to their previous customers. Ask if there is any current jobsites they have that you can take a look at.
Make sure you know what it is that your getting. Make sure you have all the promises your contractor makes to you in writing.
Ask your contractor if their work is covered by a warrany. Ask what will happen if something happens to their work. Ask if you will be charged if their work needs to be repaired.
Do not give your contractor an excessive down payment. Also do not pay your contractor for that is not yet done. This could cause the contractor to not come back to the jobsite in a timely manner or not yet. This could also cause a lack of quality in the workmanship.
Talk to your contractor and get a daily or weekly schedule for what progess is expected to be made.