I don't know what numerical amount I am supposed to put on the state tax forms.

You are your husband are residents of Utah. Utah taxes all income and gives a credit for the tax paid to Idaho. Your husband lived in Idaho for work, he was not a resident. He didn't change his license and move all his stuff there with the intent of living there forever. He was just working there.

You will need to prepare the states in a special order. You may need to delete both states and begin again.

 

1. First, prepare your non-resident  return. This creates your tax liability for the non-resident state. How do I file a nonresident state return?
2. THEN prepare your resident state return and it will generate a credit for your income already being taxed in the non-resident state.
3. The credit will be the lower of the state tax liabilities on the same income. You may owe your resident state.

It isn't possible for the program to create a credit before it knows the liability. Your returns may be wrong if you do not prepare the states in this order.

We live in Idaho and his job has him living in Utah since June and our family is still in Idaho.  Which State should I start with and how should I proceed?

You should start with Utah, since that is the non-resident state. Indicate that you are a non-resident of Utah and complete that state return.

 

Then, start the Idaho return and indicate that you are a resident of Idaho for the whole year. You will see an option for a credit for tax paid to another state, and you will be instructed to enter the tax applicable to Utah, and it may be populated automatically. If not and to confirm that the Utah tax is correct, use these menu options to view the Utah tax summary. You need to be in the Utah return when you try them though:

1. Tools
2. Tax Tools (left side of the menu bar)
3. View Tax Summary

Make sure you enter the Utah tax, not just the tax due, if any. You will get a reduction on your Idaho tax for the tax paid to Utah.