Depending on the state, you should first look for C license, insurance, bond, etc. Once you are sure they are a legit company, you want to make sure they follow the local/state codes by getting permits. You will be able to verify they did good work. Good luck
Verify that they are licensed and insured. Try to get recommendations and be careful of any company looking for a large deposit. Make sure you have a contract in writing.
For simple insulations, just make sure they are licensed and insured.
For more complex alterations involving two (2) or more different trades, make sure they have a General Building License.
For California, go here: cslb.ca.gov.