If I have multiple people on my lease, what do I put for monthly rent? Do I put just my portion or the whole amount?

Are you entering information for a a state rent credit?  You enter the amount that you paid.  You cannot claim to be paying the total rent for all the other people living with you if your roommates also pay rent.

If you are claiming a state renter's credit, enter your portion of the rent you paid, and let us know what state you are filing in.   

There is no tax deduction for rent paid on your federal return.   The rental properties section in the federal interview of TurboTax is for taxpayers that own and rent out real estate for rental income.   If you don't own rental properties, you can skip that section.