Both Sindarin and Quenya are written in tengwar and english, thouhg Tengwar is how it should be written.
The elvish used in the films is mostly Sindarin, though there are a couple of Quenya bits, like Aragorn's coronation song.
The way i am learning elvish is through the languages workbook on
www.councilofelrond.com . You have to sign up to the site to use it, but it is very good, and there is a forum there especially devoted to elvish, so you can query things there, and, I believe, have discussions in elvish.