Each person files their own return, including dependents.  Be sure to mark on that return, that they are a claimed as a dependent on someone else's return.

If the dependent has to file to get tax withheld or because they made enough income they file their own return taking care to check the box saying they can be claimed by someone else. 

If you’re using TurboTax Online, you must open a new account for your dependent’s return.  With TT Online, it’s one tax return per account.