There is nothing to claim on your income tax return for being a spouse survivor. You owe income tax on whatever your income happens to be. If your income includes a survivor's pension, that's part of your taxable income. If you think there is a state exemption to tax on the pension, you have to check with your state.
If you are providing care in your home for a qualifying person, usually a child dependent, you can use the filing status of "surviving spouse" (used to be called qualifying widow/widower). This provides some of the advantages of married filing jointly instead of single, but it only applies if you are caring for a dependent.
