As churches still do today, churches of colonial New York often kept records of birth and marriage, as well as membership. It is the vital records that best help us figure the Teator families.
However, many of the early records could have been written in Dutch, Latin, German or English. And since many of the early settlers were not literate, whoever was wielding the pen wrote down what he thought he heard (which explains the 48 ways to spell our surname). These records could have been immaculately clean or, otherwise, to put it nicely. Many individuals or groups have transcribed these records into indices but one of the most prolific has been Art Kelly of Rhinebeck.
Kelly's work can be found at http://www.kinshipny.com. Dozens of churches' records have been transcribed as faithfully as Kelly could, and are available at libraries or are for sale. These church books sometimes are a record of the marriages only, or births only, or a combination. In addition, Kelly has dozens of other books available also.
One of my favorite church books is the Baptismal Record of the Reformed Church, West Copake, NY, 1783-1899. In it, Art Kelly has recorded the name of the infant, the baptismal date, the parents' names, the birth date, and sponsors' names (info blank if not known). The sponsors are similar to our godparents.
These entries are numbered for the sake of indexing, a deed that has made my life, and the lives of many genealogists, easier. A special thank you goes to Art Kelly.
Record #510, for example, lists a child David, born to parents Hendrick Tieter and Anna Vinger on 6.13* (June 13). The baptismal is on 5.29 in the 1791 section. Thus, David's baptism is May 29, 1791. And this listing of names goes on for 2905 records, with an index in the back of the book by parents and by sponsors. And, as I said, there are dozens of these books. Different spellings of the same surnames are often bunched under one of the most commn spellings. Our surname is often found under Teator.
I put an asterisk by David's birth date because something unusual happens. David's birthdate is June; his baptism is May. It cannot be in the same year. Could it be a mistake by the pastor? Could Kelly have made a mistake in transcription. Or, can one assume that David was born in June of 1790 and was baptized nearly a year later. After checking, the second choice is ruled out, the first one can never be checked, so I go along with the third one, for now, that David is born in 1790. More about the importance of sponsors in the family group page.