New Owner On Used Computer

Did she also give you the original "system restore" disk that came with the computer? It's best to start over and reinstall the original factory system and software so that it's just like new, so that none of her previous information exists on the computer and you get to put all your own passwords on it with no risk of either of you accessing each others' accounts.

no old infor is still there

Any applications that she purchased with her Apple ID are forever tied to her ID.

That's a good example of why it's best to reset the computer to factory settings and start over by entering your own name and password. There are many more areas of the system where if you don't reset the accounts, you may find parts of her information on various accounts getting mixed in with yours, and as you enter more of your own information it may get mixed in with hers. So it's best for both the previous and current owners to start off fresh.

If it's a recent OS X then you don't even need the original disks to do this. Use the OS X System Recovery procedure to do a fresh reinstall of OS X and ensure that your account information throughout the computer is completely your own.