As far as the Church of England was concerned the important date was the baptism of the infant (usually in the first few weeks of life) and this is the date recorded in parish registers. Sometimes the birth date (or age) would be added by a helpful cleric - particularly if the child was no longer an infant at the time. This means that before civil registration started in July 1837 it is often impossible to determine the date on which someone was born because the matter was not considered important enough to record.
However there were exceptions. The Society of Friends do not baptise their children but have kept excellent records (see My Ancestors were Quakers). In addition, at about the start of the 19th century people who had not been baptised began to find that there was no easy way of establishing their age (for instance in determining liability for military service). As a result the children of many educated non-conformists had their children's births registered in London with Dr William's Library. You might also be lucky in that a family bible, with birth dates written in, has survived and can be located.
Civil registration started on 1st July 1837, and while most children's births were registered this did not become universal until 1875 and error in the registration process can add to your problems (see A Comedy of Errors).
The information recorded is:
When and where born
Name if any
Name and surname of father
Name, surname and maiden name of mother
Occupation of father
Signature, description and residence of informant
Signature of registrar
Name entered after registration
The only practical way to get a certificate and find out what it says is to purchase a copy (see civil registration). Applications for Hertfordshire birth, marriage and death certificates can be made at Central Registration Certificate Archive is to be established at The Old Courthouse, St Albans Road East, Hatfield, Hertfordshire AL10 0ES. For details of ordering online see How can I get a copy certificate.
If you are having hit a brick wall in relation to an illegitimacy you may find the answer to HORN, Little Gaddesden, late 18th, early 19th century helpful.
Sometimes a direct documentary link between an adult and their birth details cannot be made. See Is this the right birth/baptism? for an example of how clues can be assembled.
Update July 2012