How Far Back Can You Get?
Leaving aside questions of how patient, resourceful and lucky you are this, really depends on what sources of information is available.
The British Isles has very extensive records, which are held in a variety of national and local collections.
In England and Wales you should be able (especially if you are lucky to be blessed with a set of unusual surnames in your family) to trace your family roots with comparative ease back to 1837 when civil registrations of births, marriages and deaths began.
Getting back beyond 1837 normally relies mainly on the use of parish registers – with luck, and allied to other types of records, these might enable you to trace your family back to the late 16th century.
Beyond this can be extremely difficult, unless you can tie in to a well-documented pedigree, for example of royalty or a great land-owning family. Also many records pre 1700 are in latin.