Answer:
Please note: the answer below is a spoof. Continue in your search, or you will sound ignorant to those who know that to err is human. To 'air' is just careless.
You would, ideally, pronounce the word as when saying 'air.' Though upon first glance, it may seem as 'err' is prounced as if you were slightly confused and merely making a noise to fill a space of awkward silence, 'err' is also seen in the much cliched phrase: "to err is human." In this phrase, 'err' stands for the first part of 'error' which gets a sound much like sayign the word 'air' which brings me back to my original point.
Or, you could say it with a slight British accent that is a cross between the two pronunciations. Then, you would seem to have a mysterious, sophisticated air similar to that of an English professor at Oxford.
Or, even better, you could just race through the word and hope that no one notices. :)
So I thought I should clarify: I don't normally talk like that big paragraph I just typed. I just wanted to write like a know-it-all snob. Fooled ya! XD