Ask around for referrals. Your friends may have had a good - or bad - experience with someone. Either way, write down the name.
Ask at your local wallpaper store. But remember that in some cases - like at the mega home-improvement centers - referrals may include a commission arrangement with the store. There's nothing wrong with this practice (if the paperhanger does a good job), but it may raise the price a little bit.
Ask craftspeople you respect for their referrals.
Remember that you can't get an accurate estimate over the phone. A good paperhanger will always come to the job site and see the space firsthand. A smart homeowner will want to look the paperhanger in the eye.
Check the paperhanger's references - call one or two. But be aware that no craftsperson will give you the name of someone who wasn't pleased with the work.
Go see examples of the work, if a reference will let you come over.
Be sure the paperhanger has a license and construction insurance, if required by your state. Both the state and the contractor's insurance company should be able to provide this information.
Get bids in writing. Each proposal - or contract - should be written in clear, ordinary language, with a payment schedule clearly laid out.
Get a start date and a completion date.