On July 1, 1837 a national system called Civil Registration was introduced for the registering of births, marriages, and deaths in England. Some other European countries have similar systems of the same name. There is a national index broken down by year and quarter and then organized alphabetically. The certificates have not been microfilmed and must be ordered from England.
Birth certificates include information such as date and time of birth, place of residence, parents names, and occupation of the father. One especially nice thing is that the mother's maiden name or previous married name is recorded. If a mother's name was written Mary Jones formerly Smith late Carter, it would mean that her maiden name was Smith and her last married name was Carter. Having this information makes a marriage search for the parents a lot easier. If you do not find an ancestor in the index to Births, among other things it may have not been reported. Up until 1875 when heavy penalties were given for not reporting births, a sizable percentage went unreported.
Marriage certificates were filled out at the time of event with a marriage official present and were therefore more likely recorded. Marriage records include information on the date and place of ceremony, the names and ages of spouses, place of residence, occupations and conditions (bachelor, widow, etc.) and the names and occupations of fathers. If the father was dead, it was often mentioned as well. Marriages are indexed under the names of both husband and wife. A few people were married in romantic locations such as Gretna Green, Scotland, which could possibly make your search difficult.
Many researchers don't see the value of Death Certificates, but in some instances they can be highly valuable. The basic information given on the record includes name of deceased as well as date and place, the cause of death, age of deceased (from 1865 onwards) and occupation. If the deceased was a woman or a child, then often the husband or father was also mentioned, providing valuable linkage information.
In general, always pay attention to names of informants and witnesses, which are usually relatives. Also, if you can find a certificate for your ancestor near a census year, it could really aid your census search. British censuses are far less indexed than U.S. censuses and there are street indexes for some towns.
The Civil Registration index is available at several repositories including the Family History Library in Salt Lake and many of it's branches called Family History Centers. There is also an ongoing project called FreeBMD that is putting the index online. It is not complete, but it has come a long way and a large percentage of entries are online. Check out their website at freebmd.rootsweb.com.
Certificates can be obtained through the General Record Office in London, where the records are centrally located. Their website is www.statistics.gov.uk/registration. Other researchers are often willing to get the certificates for you in person, which can be less costly.