First, you must be appointed as her personal representative. This may require going to your local probate court, especially if she did not have a will (but even if she had a will, you have to go to court and get officially appointed.)
Then, you would prepare a tax return in the normal way. Her income from January 1 to the day she died is reported on a regular tax return. There is a place to check a box for "the taxpayer died during the tax year." After completing the return, you need to print and mail it, and sign for her as "personal representative." If she is owed a refund you will need to include form 1310 so the refund can be paid to your bank account.
https://www.irs.gov/individuals/deceased-person
https://www.irs.gov/individuals/file-the-final-income-tax-returns-of-a-deceased-person
https://www.irs.gov/forms-pubs/about-form-1310
If she had ongoing income after her death, then you probably also need to file an estate tax return. You would have to provide more information.
