Many states have an online tracking system for checking the status and whereabouts of your ballot.
Go to the State Voting Information Directory - choose your State hit submit. Then click "State Look up Tools" to see the list of state-specific tools. There you will see a link to "Where's My Ballot?" - if your state offers such a service. This should tell you if your ballot request was approved, and if your ballot has been sent.
If your state does not offer ballot tracking, you may need to call your election office. To find your local election official, please look up their contact information in the Election Official Directory.