How is the best way to determine that the James Hay that married Elspet Forsyth is the one baptized 06 March 1760? As I indicated, I am a raw amateur at this.
I think you are perhaps starting with the wrong question. You need to ask, "How can I find out who were the parents of James Hay who married Elspet Forsyth?"
You have to bear in mind that there may not in fact be any surviving record of James Hay's baptism. You must not assume that just because there is one born about the right time in the same county, he has to be yours.
First of all, consider the names of their children, in order, because this might give you a clue to their parents' names. I think you have already done this. The children listed on FamilySearch are
Elspat, 1785, Duffus
William, 1787, Duffus
George, 1798, Duffus
Alexander, 1811, Elgin
Unfortunately there are huge gaps; 11 years between William and George, and 13 years between George and Alexander. There is no way of knowing whether these are genuine gaps, or whether there were other children whose baptism records have not survived, or who died before they were baptised. So other than suggesting that James Hay's father might have been a William, this approach isn't going to work.
Have you got all four of the full baptism records? If not, you need to get them. They may contain some sort of clue - a witness named Hay with where (s)he lived, for example. The best thing would be to go to somewhere where you can rent a copy of the microfilm of the Duffus parish register and read through it looking for Hays who are listed as witnesses to baptisms, noting their names, the dates, where they resided and who else were the co-witnesses. If you are lucky, you may be able to build up a picture of where the Hays resided, and who their friends and neighbours were.
Go to LIBINDX and just put in the surname Hay and then in turn look up the ones born, married or died in Duffus. If any of them died after 1855, get their death certificates and seen what that adds to the collection of information. You might get lucky and find a death registered by a first or second cousin that might give a clue. There is, for instance, a Jane Hay, wife of Robert Gray, who was born in Duffus and died in Elgin in 1879 aged 87. Could she be another child of James and Elspet? Did she have children? Who were the witnesses at their baptisms? Is she the same person as Ian Gray, maiden name Hay, who applied to Elgin Parochial Board in 1878? If so, her application, available from the Moray Local Heritage Centre, will provide quite a lot of information about her and her origins, and her death certificate should name her parents.
Have a look through the Duffus Kirk Session records to see if any Hays were mentioned there. This isn't an easy job, because you have to go to a repository where you can access them and the sit and peer through pages of digital images. Make a note of anything you find relating to Hays, with the date, residence and anyone associated with them.
Look in the 1841 and 1851 census at FreeCEN to see if any of your Hays are recorded - maybe one of them might be living with a cousin or other relative.
Putting together all you can find out about the Hays in Duffus might just begin to show patterns or pointers. It won't be easy, and it may take a long time, but you may be rewarded.