Hi! Happy to assist!
Your federal tax return, you have the option to file married filing jointly or married filing separately. If you have any dependents and decide to file separately, dependents will be claimed by the parent they live with (other rules apply). If filing jointly, you would include your total income from both states.
You state returns might be a bit more complex.
For the first year, One of you will be a part time resident of state A and part time resident of state B. The other spouse will only be the resident of only one state, since they are not moving.
If your states allow, you may file married filed separate returns for each, however, this is a bit complex and the best way to do it would be by using TurboTax Desktop.
Here is the link with more detailed instructions: