A beginner's guide and some UK resources

There are many beginner's guides available, All of the major genealogy websites has at least one. A reader of this site, recommended this one. I like the fact that is very general in nature, and is aimed at total beginners. 

Genealogy & Ancestry Guide – Finding Your Family History

Although it is hosted on a UK site, the article refers to the US sources.

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Most of my recent research has been in England and Wales, which has some excellent free resources.

FreeBMD is free and there is no need to create an account.  - Is an index to Births, Marriages and Deaths since 1 July 1837. I find it especially useful for finding the maiden names of females. From the UK censuses you can usually estimate when and where a couple was married. I usually look at the age and birthplace of the oldest children listed in the census, as a starting point. Then in FreeBMD, I look for the marriage of a man by the father's name, in that locality during the preceding 5 years, Since you now know the mother's maiden name and approximate year and locality of her birth, you can research her genealogy.

The General Register Office index  requires a free account and is more awkward to search, I find it useful for finding the maiden surname of the mother before the time period when this is given in FreeBMD. I can also find the birth registrations of the children, including those that may have died before their first census.

UKBMD gives access to a variety of UK sites that can be useful such as OPC - Online Parish Clerks, 

FreeREG can give you access to the entire contents of the official record if this site has it, It is worth a try, but remember that FreeBMD has an index of essentially all births, marriages and deaths from mid 1837, to the latest dates made public. FreeREG is limited to the records that people have added. A major strength of FreeREG is that it includes Church of England records prior to 1837, as well as government (GRO) records since that date. 

FamilySearch has extracted the data from thousands of UK parish registers. Everything on the site is entirely free, but does require registration, Unlike the other sites I have listed, FamilySearch has records from all over the world, 

A relevant bit of UK history:

When King Henry VIII broke with the Roman Catholic Church, he established the Church of England, as the state church and the state department of social services. The local parish was expected to minister to the spiritual and physical needs of the king's subjects living within the parish boundaries. Starting in 1538, each parish was asked to keep a record of christenings, marriages and burials, Unfortunately, many of the older parish registers have perished over the preceding 500 years, but it is not uncommon to find them going back into the 1600s. Members of the aristocracy can sometimes be found in even older records (e.g. lands and titles), but for common people there are almost no records going back further than this. In 1837 the government assumed the direct responsibility for keeping a record of all births, marriages, and deaths in England and Wales, This is the role of the General Register Office.

Scotland and Ireland have their own institutions and their own resources.. 

I hope you enjoy finding your ancestors!