I am looking for the birthplace and parentage of Ambrose Sayward , born cir 1805 and died in Burnham, Maine 14th Mar, 1875. He is buried in the Reynolds cemetary in Burnham, Maine.
First step, since you know the date and place of death is to research the place of death for other clues or relations.
Burnham, Maine has an information page that has various links that may be of interest. If I go to the 2nd page of the death record, I do see four people named Sayward who passed away between 1916 to 1934 who may have been relations. If they were, their birthplaces may lead to the birthplace of Ambrose.
If this is the picture of Ambrose's cemetery stone, then it identifies Ambrose's birth as around July 1805 which narrows it down a little more. His wife would then have been Martha Sayward. Can you find information about Martha? Maybe you can track down where they were married?
There might be records with the church or cemetery where he is buried.
These are a few ideas that might allow you to go further.
You don't say what research you've already done.
If you haven't done so already, you should search for him in the US censuses. Don't be too prescriptive about the birth date or the spelling of his name. FamilySearch.org is one place you can search free of charge. Even though the censuses don't give you detailed information about his birth, they can help you locate him in different places through time, which may help. I would also investigate what other Saywards were living in and around the same place as Ambrose; if you can identify a likely sibling, that gives you another route to identify the parents.
You should also search for a marriage record for Ambrose, which should also contain useful information. (I presume he was the Ambrose Sayward who married Martha Sayward also buried at Burnham, Maine).