I can vouch for
http://www.elvish.org/FAQ.html - the website looks utterly archaic but the editors are well-respected academics and scholars. After the FAQ, though (which does a good job of explaining the limitations involved in learning
Quenya or
Sindarin - the tl;dr is that
Tolkien himself changed his mind quite a lot about how the
languages ought to work, and thus there are sometimes multiple competing variants; there is no one, authoritative, guide to all of Quenya grammar, for example), you may still want to check out some of the courses that are available online.
These vary greatly in quality (some are rubbish), but two that I can recommend:
Helge Fauskanger is a Norwegian linguist, and a very good one, who maintains a website on Tolkien's languages here:
https://folk.uib.no/hnohf/ He has a free (Neo)-Quenya course which is available here:
https://folk.uib.no/hnohf/qcourse.htm
There is also this website, maintained by Thorsten Renk, a German linguist:
http://www.science-and-fiction.org/elvish/index.html There is both a (Neo)-Sindarin course (
http://www.science-and-fiction.org/elvish/index.html#course_sindarin) and a (Neo)-Quenya course (
http://www.science-and-fiction.org/elvish/index.html#course_quenya)
To be clear, both of these websites present a 'reconstructed-by-academics-from-available-evidence' and thus inevitably artificial form of the languages. (When Tolkien has not specified how a particular point of grammar works, for instance, some educated guesswork is required! And Fauskanger and Renk do not always agree in their interpretations.) However, they are both respected scholars who have worked very closely with the available sources and if you are looking for help, I would start with them.
There are also some
books available, but most of them are now out-of-date: Ruth S. Noel's
The Languages of Tolkien's Middle-Earth is painfully dated and frequently just plain wrong. David Salo's
A Gateway to Sindarin might be helpful, though, if you would like to study Sindarin as it is presented in the Jackson films (which is also a reconstruction, by Salo).
