When a person dies a record must be made of the death and filed away in the government paperwork. All states make their death records available for free to the public because it is a public document. However, many times when you attempt to search these documents via the Internet you find search engines which are decidedly not free. As such, you should be careful where you look and just how you go about your search.
Gather all of the information of the person whose death certificate you're looking for. Their name, last address, social security number, age, year of death and anything else that might help you identify that particular record.
Find an online search engine that allows you to search death records. Search.usa.gov is the official search engine for U.S. public records, but other search engines like snoopstation.com may also yield the death certificate that you're looking for.
Once you've found (or think you've found) the death record you're looking for you should call the courthouse in that area to check it. This is especially true if you want a copy of the record sent to you, which will cost a copying fee in most courthouses, along with a mailing fee.
There are a lot of search engines that will charge you money to look for public records. The records are free and so is access. Make sure you're not paying for the service.