You will file his taxes on the same form that would have been used if he were alive, but Deceased will be written at the top. Report all income up to the date of death and claim the deductions and credits that he would have been eligible for. You will sign the return and note that you are signing on behalf of the decedent. If there is a refund, you will need to file Form 1310, Statement of Person Claiming Refund Due a Deceased Taxpayer with the tax return.
For more information, refer to the TurboTax articles Death in the Family, Can I e-file a tax return for someone who is deceased?, and Can I file Form 1310 in TurboTax?
Please accept my sincere condolences for your loss.