Have a good reputation? Check for references and call a few of them.    

Have adequate insurance coverage? Protect your home from accidental damage?

Thoroughly inspect your roof? Including flashing chimney, soil stacks, other roof penetration, deck, plus attic?

Provide a written estimate? Including an accurate description of the work to be performed, plus work that may have to be contracted out?

Explain the entire project process? Your project is most likely a series of components that work together; you should know all about them.

If it is a roofing project, do they check existing ventilation for proper circulation? Explain the importance of ventilation? Improper ventilation will damage your shingles and can invalidate your manufacturer's warranty.

Explain reasons for tearing off versus nailing over existing materials?

Know, explain and comply with local building codes?

Apply underlayment? Additional waterproofing underlayment might be needed.

Apply products according to manufacturer's specifications?

Use proper fastening techniques?

Commit to supervise the job during all phases of work and inspect it completely when finished?

Thoroughly clean up when finished? Remove all surplus material? Leave your yard in the same shape the contractor found it?

Clearly explain both the workmanship and manufacturer's warranty? Are defective shingles replaced for prorated replacement cost, or original cost, with labor additional? You should be very clear about who to call with a problem.

Offer any additional warranty coverage?

Use quality materials? Check warranty plus UL fire and wind resistance ratings. Choose a name you trust - not all products are the same.