How do I start a new return for my Mother?

TurboTax Online allows you to file one return per account. You would have to create a new account for each additional return.

TurboTax Desktop (Download/CD) allows you to e-file up to 5 federal returns, and unlimited print/mailed returns.

TurboTax Desktop can be purchased here: TurboTax Desktop Download Page

Online is only good for 1 return.  But you can use the same email address for 5 accounts.   How to start another return in the Online version https://ttlc.intuit.com/replies/3288574