From the SSA website:
When you die, certain members of your family may be eligible for survivors benefits. These include widows, widowers (and divorced widows and widowers), children and dependent parents.
Who can get survivors benefits based on your work?
Your widow or widower may be able to receive full benefits at full retirement age. The full retirement age for survivors is age 66 for people born in 1945-1956 and will gradually increase to age 67 for people born in 1962 or later. Reduced widow or widower benefits can be received as early as age 60. If your surviving spouse is disabled, benefits can begin as early as age 50.
Your widow or widower can receive benefits at any age if she or he takes care of your child who is receiving Social Security benefits and younger than age 16 or disabled.
Your unmarried children who are younger than age 18 (or up to age 19 if they are attending elementary or secondary school full time) also can receive benefits. Your children can get benefits at any age if they were disabled before age 22 and remain disabled. Under certain circumstances, benefits also can be paid to your stepchildren, grandchildren, stepgrandchildren or adopted children.
How do I apply for benefits?
If you are not currently getting Social Security benefits
You should apply for survivors benefits promptly because, in some cases, benefits will be paid from the time you apply and not from the time the worker died.
You can apply by telephone or at any Social Security office. We will need certain information, but do not delay applying if you do not have everything. We will help you get what you need. We need either original documents or copies certified by the agency that issued them.
The information we need includes:
Proof of death—either from a funeral home or death certificate;
Your Social Security number, as well as the deceased worker’s;
Your birth certificate;
Your marriage certificate, if you are a widow or widower;
Your divorce papers, if you are applying as a divorced widow or widower;
Dependent children’s Social Security numbers, if available, and birth certificates;
Deceased worker’s W-2 forms or federal self-employment tax return for the most recent year; and
The name of your bank and your account number so your benefits can be deposited directly into your account.
What if I work?
If you work while getting Social Security survivors benefits and are younger than full retirement age, your benefits may be reduced if your earnings exceed certain limits. (The full retirement age was 65 for people born before 1938 but will gradually increase to 67 for people born in 1960 or later.) To find out what the earnings limits are this year and how earnings above those limits reduce your Social Security benefits, ask for How Work Affects Your Benefits (Publication No. 05-10069).
There is no earnings limit beginning with the month you reach full retirement age.
Also, your earnings will reduce only your benefits, not the benefits of other family members.