How would I go about taking another person to small claims court if they live in another state?

If your contract with the other person was entered into in the State that you live in now, service of the complaint by certified mail should be sufficient to perfect service regardless of where he now resides.  Collecting the judgment will be more difficult as the Court will not have jurisdiction over the assets in another state and you will have to domesticate the judgment in the other State and pursue collection pursuant to the other state's laws.