How do I add my spose to a business under the "Tell us the type of self-employment work you do?"

As a partner?  You either have to file a separate partnership return  or do a separate schedule C for them and split the income and expenses.  Self employment is 1 person.   And it depends if you are in a community property state.  I'm not sure how all that works.  

If you need to switch the owner of Schedule C to your spouse, you can make that change on the General Info screen.   Each Schedule C is assigned to only one taxpayer.  Click Edit underneath the owner's name and change it to your spouse.  

 

 

You can choose your spouse on the next screen.