There are several factors that can complicate multi-state returns.
1. The move involves more than 2 states.
2. There was no move, just a change in work location to one or more states outside of your home state.
3. Working in one state while living in another.
4. Spouse who works and lives in another state.
5. Spouse who has never even been in the state you live and work in.
These and other issues can complicate the preparation of your state return. Each scenerio is unique and should be analyzed for pertinent details of when and where you worked. Weeks of unemployment can also add to the complexity. Create a spreadsheet that allocates your work by time and state. Keep a calendar of jobs in multiple locations so you can use it at the end of the year for your worksheet. Be consistent in your method of allocation.
Sometimes, the company allocates the work for you and gives you w-2s that indicate how much was earned in each state. That is the easiest method. But sometimes you work for more than one company.
The important thing to remember is you shouldn’t have to pay twice for the same income and if you do then there is normally a credit for taxes paid to other states on your return that you should claim against the duplicate income.