When Elendil arrived on the shores of Middle-earth in S.A. 3319, Gil-galad, the High King of the Noldor Elves had been at war against Sauron for some 1500 years.
And because Sauron feared Númenor, he feared Gondor and Arnor. When Sauron attacked Gondor in 3429 S.A Elendil and Gil-galad formed as an answer to this common threat the Last Alliance of Elves and Men.
In Arnor the two kings gathered their armies and set out for Mordor. In S.A. 3434 they defeated Sauron's army in the Battle of Dagorlad. And then they breached the Morannon and fought the final battle on the slopes of Mount Doom (S.A. 3441) in which Elendil and Gil-galad perished, but Sauron was slain by Isildur, Elendil's eldest son with the help of the shards of Narsil.
Although the Last Alliance of Elves and Men ceased to exist after this war (due to the lack of a common enemy and the waning of the Elves) there always was a strong friendship between the Dúnedain and the Elves.