Nonconformists did not worship in a parish church, preferring a chapel or meeting house, meaning you may not be able to find them in parish registers. Originally, these chapels were private buildings put to religious use. They did not have burial grounds so the dead had to be buried in local churchyards. This changed with the implementation of the Toleration Act of 1691, which meant nonconformists could set up burial grounds. Until 1689, attending a church service in an Anglican Church was mandatory, and if a person did not attend, they could have been fined or had their lands seized.
Most congregations kept books of births and marriages, and after 1691, burials. These registers were either kept by ministers who went round to each chapel, or by the individual chapel. They were not considered admissible by a court, so you may find the baptisms of the children of your nonconformist ancestors in a local parish church. Baptists opposed infant baptism, so you may find this is not the case if you have Baptists in your family.
Nearly 50,000 baptisms were registered in the General Register of Births of
Children of Protestant Dissenters at Dr William's Library in Red Cross Street,
Since 1837, the births, marriages and deaths of nonconformists are included in civil registration records, but before this date, they are not so easy to trace because each branch of nonconformism had their own chapels and kept their own records. You will first need to discover the religious body your ancestors belonged to, and then find if any registers survive.
Some nonconformists kept birth, baptism, marriage and burial records from the late seventeenth century, but many chapels have no surviving registers until much later. Many marriages, however, had to take place in the Anglican Church after 1754, when Hardwicke's Marriage Act was introduced.
It is possible to search through some Non-Conformist and Non-Parochial Registers on-line.