I work in a different state than I live in, do I have to pay taxes in both states?

If you are present in a state, then any income earned during this period, must be reported to the state.

To your resident state, you must report your worldwide income for the year. Read about taxes involving two or more states: Your U.S. Tax Return: Working or Living in Two or More states

You have to file tax returns for both state (unless the states in question have an agreement to do otherwise), but the state in which you LIVE will normally give you a credit for the taxes you paid to the state where your worked. This avoids any double taxation.