In addition to family Search which I agree is a good place to start, if your ancestor was born after March 1837 then an important additional search would be at the GRO website.https://www.gro.gov.uk/gro/content/certificates/default.asp (need to register but free) Thie index of birth registrations includes the mother's maiden name. For the earlier period, this is not available elsewhere
Before BMD registration in 1837, and the census which started in 1841, a major source are the parish registers (recording baptisms, marriages and burials) A tip is to google, ' name of parish ( I used Charminster) records family search' The result was this https://familysearch.org/wiki/en/Charminster,_Dorset_Genealogy which includes a chart showing what parish records are available online for that parish.
Freereg. is a volunteer site which indexes and partially transcribes parish registers . Even if the same record is indexed on Family Search, the Freereg index is often better .They include detail that the Family Search index doesn't ( can include occupation, witnesses, fathers name and occupation and any odd notes in the register) The coverage is patchy but in some parishes can include registers going back to 1538.
A third useful source are the online parish clerks. Again run by volunteers, they are all very different (and some areas don't have them) They can include parish registers, census transcripts and sometimes abstracts of wills and other records I'm mostly familiar with West Country OPCs. As examples, here are two that I find very useful Cornwall OPC, Dorset OPC . To find them in other parts of the Country google the name of the County + OPC.
Lastly what you can find without payment varies. Lincolnshire archives has put many of it's images online and they are available freely (though quite hard to search) Essex has an excellent search engine and has also digitised many images but they operate on a pay to view basis.
There are of course the major subscription sites, the 2 main ones Find My Past and Ancestry have full sets of census images (Family Search has only partial transcriptions) but after that they differ on what parish and other records they hold. (personally I find ancestry better for my purposes that FMP but that's because they hold the licence for images for the counties I have most interest in)