First of all allow me to express my condolences on the passing of your loved one.
The tax filing status after the death of a loved one is fairly straightforward. If your spouse dies during the year, the IRS considers you married for the entire year and you can use the filing status "married filing jointly" when your tax return is prepared.
On the top of form 1040 for your loved one, write "deceased" and your spouse's name and date of death. If there is a personal representative that has been appointed for your deceased spouse, then that person will have to sign the return and if the return is a joint return, you will also sign it. If there is no personal representative then you should sign the return and in the signature area write "filing as surviving spouse".
For the two years following the death of your loved one, if you have a dependent child and meet all the requirements listed below, you can use the filing status "qualifying widow with dependent child".