Without someone else having written our genealogy, loaded with sources documenting the finds, the average person will look at a bunch of church records with a lot of familiar names. As you have seen earlier, though, there are a core of common names, and it is possible to have several people of the same name living in the same area having children. Just because Hendrick has a son named David in one record, and thirty years later David has a son named John, does not make John a grandson of Henry. How do we know that John's father is the son of Henry? How do we know that the son David is the father David?
The simple answer is that sometimes we may never know. There are, however, some excellent leads which may point to an overwhelming circumstantial conclusion. Let's look at one such family, this one made much easier because all the children are found in the same church book (as opposed to the common possibility that several churchbooks are needed). Also keep in mind that the church book may not be the place of residence of the family; it is simply where the baptism is recorded. (Thus, your family could be living in Durham, have the baptism actually done in Oak Hill, but be recorded in the Middleburgh book!)
Hendrick Tieter and Anna Vinger have David (b. 13 June 1790, bpt. 29 May 1791) at West Copake. Sponsors are David Vinger and Elisabetha Dick.
Hendrick Tieter and Anna Vinger have James (b. 25 Feb 1793, bpt. 8 Jun 1793) at West Copake. Sponsors are Zacharis Tieter and Eliz. Weelen.
Hendrick Dieter and Anna Fingar have Johannes (b. 12 Jun 1795, bpt. 9 Aug 1795) at West Copake. Sponsors are Joannes Fingar and Critje Whealer.
Hendrick Dieter and Anna Fingar have Zacharias (b. 8 Sep 1797, bpt. 12 Nov 1797) at West Copake. Sponsors are Zacharies Dieter and Sarah Dieter.
Hendrick Dieter and Anatje Finger have Marcus (b. 9 Aug 1799, bpt. 25 Aug 1799) at West Copake. Sponsors are Marcus Dieter and Lena Finger.
Hendrich Dieter and Anna Finger have Philip (b. 18 May 1801, bpt. 14 Jun 1801) at West Copake. Sponsors are Philip Kuhnst and Eliz. Finger.
Hendrick Dieter and Annatie Vingar have Mary (b. 18 Jul 1803, bpt -no date given-) at West Copake. Sponsors are David Hess and Mary Vinger.
*** There are other Henry Teters and other Anna Fingers in
the area at that time, although none are married to each other
that I know of. So, how do we know these children go with these
parents? For one, the names Henry and Anna together are an obvious
clue. A second clue, at first, not seeming so important, are the
sponsors. Often, the sponsors are relatives, and these in turn
may prove linkage in the sponsors' family when the sponsors have
children. Often, the sponsors are a married couple.
Another little interesting piece is a naming pattern. A researcher should consider the possibility that the grandfather's and grandmother's names are used for naming the grandchildren, as are the names of the parent's siblings.
A close look would reveal the following: Mary's female sponsor is Mary Vinger, Anna's sister. David's sponsors are Anna's parents (Contrary to expected, many times the first son may be named after the father's father, but not in this case.) James is sponsored by Henry's parents. In each of the other cases, each child is named or is sponsored by a sibling or aunt or uncle of the parent. Cross-referencing these connections across families often gives substantial proof about our findings of families.