If your person died after about 1963, they should show up on the SSDI (Soc Sec Dth Idx).The computer index was begun about 1963, so anyone who died earlier won't show up on that index.Here is the site for the SSDI:
On the left side of this main page there is a list of states, click on one of your choice.Then find and click on county of your choice.The goal of this project is to get all cemeteries across the country online.Some counties may only have a list of their cemeteries, while others will havenames of everybody buried in their various cemeteries.Most sites will have a search feature, be sure to use it.Some counties will have censuses just for their county online, list of early land owners, tax lists, early marriages etc.It will be hit and miss what they will have online, but always check back from time to time as most are adding new information.Post queries on those sites, you never know who is using which sites, so post everywhere you can.(^_^)
I don't know why, but counties will also have an archived site, some will contain basically the same information, others will have more then the county site itself.Here is the site to find those archives:
If youhave U.S. research be sure to bookmark these sites.Some states have good information, too.TX is one, be sure to check out links like TX Research Help.It will have a list of links to other "goodies."The Handbook of TX is one, and there will bemuseums, archives etc.Click and look of some of those links, you may not need them right now, but you will have an idea of what is available if you have a need later on.
If you do not have a subscription to Ancestry.com (I don't), you local Family History Center has one, and their volunteers will help you learn how to use it.Lots of good stuff on there for beginners.Check with local public libraries in your area, some have a subscription to Heritage Quest.HQ has "some" censuses indexed, a name index to over 25,000 published histories, PERSI, and they just added Rev War pension records.With a library card and password, you can go online from you own computer at home.This one I do have from our local public library.Only libraries can subscribe to HQ.FHCs do not have this one.
If I didn't make this clear, or you have any questions, don't hesitate to ask.