How was the element nitrogen first isolated and by whom?
Your question is interesting just because you did not ask who "discovered" nitrogen, but who first isolated nitrogen. Still, the answer is the same. We commonly think of the Scottish man named Daniel Rutherford to have BOTH discovered AND isolated nitrogen in the late 18th century.
At that point Daniel Rutherford called it "noxious air." He did NOT, however, distinguish it as a different chemical substance and name the element (which was done a few years later by a different scientist). He just isolated it and "distinguished it" from what he called "fixed air."
The "how" in regards to the answer to your question is that Rutherford demonstrated that there was a certain part of air that didn't allow things to burn. It was this "noxious air" that Rutherford showed did "not support combustion," which is just a fancy way of saying that things don't burn when exposed fully to nitrogen.
Oxygen, of course, is needed to burn things. It is a bit ironic that Rutherford only just beat out three other scientists in this discovery: Scheele, Cavendish and Priestly. Further, it was a French chemist called Lavoirsier who actually named the element "nitrogen" in 1776.