
Image source: http://www.singaporecarpet.com/images/carpet-installation3.jpg
First and foremost, find a way to get referrals. Real referrals. There are online companies that do nothing but match new customers with experience and qualified contractors of all types. Current and previous customers even get the chance to post reviews and go into detail about the projects they did and how they came out.
Many contractors are required to be licensed by the state they work in. Usually this is not true of carpet installers, only full service building contractors. However, all real businesses are required to register with the state and probably get a DBA designation. Ask your installer if he is registered and ask for proof. Some states allow you to do these checks on line, too. Be careful about doing business with someone who is not registered. If he is hiding from the state, he has something to hide. Find someone else.
Newer carpet installation companies tend to be a step above the old fashioned carpet installer who showed up with hammer and nails and not much else. These new companies will arrange in home consultations at your convenience, for no charge, and they will help you select carpet, choose styles to match your current or planned decorating schematics, discuss soil and water proofed fabrics, and help you coordinate colors. If you can find a company to do this, take full advantage of their services.
One pet peeve that carpet installers have is that when they show up to lay carpeting, home owners assume they are also going to clear the room of furniture. No. Don't plan on it. Their liability insurance won't allow it, they don't want to, and your home insurance probably won't cover it if something happens. Do it yourself. Long before they get there, too. They don't want to show up and wait two hours while you round up neighbors to help dismantle your king sized bed and fish tank.
Before signing anything, read it thoroughly. You don't want surprises in the end. Also watch out for people who ask for cash deposits. If you give them money and they never return, you have no recourse. Stick with companies who take credit cards. At least your credit card company will give you a refund if you don't get your carpeting. Nothing hurts a contractor like losing money.
Next, find out how he pays his employees. If he doesn't pay them, the employees may be able to place a lien on your home - even if you paid the boss.
Finally, talk about insurance. He should have some type of liability or workers comp insurance and he should have an insurance certificate to prove the coverage is current. Don't assume your insurance will pay for mishaps - this is the last thing you want.