On A-U there's an Elvish section where you can learn useful elvish phrases like hello, and goodbye.

How do I learn Quenya and Sindarin?

That depends on what you mean by "learn". If you mean "learn" in the sense in which one can "learn German" or "learn Japanese", then the short answer is that you can't; see the previous question.

If you mean "learn" in the sense of "learn Gothic" or "learn" any other fragmentarily-preserved, non-living language, then one answer is to read well-researched, thoroughly documented, purely descriptive articles and discussions about the languages, based upon Tolkien's writings and free from artificial, utilitarian agendas; and to do so in conjunction with an independent examination of the data cited to verify claims. But the best way to engage with Tolkien's art-languages is to simply study this evidence for yourself, to read and ponder Tolkien's own compositions and commentaries.

It must be remembered that Tolkien is the sole and final authority on his languages; anything not written by Tolkien is strictly speaking not Quenya or Sindarin, but is simply more or less reasonable conjecture based on a selective set of data and supposed facts derived from them.

FAQ E.L.F.

So my short answer is: that I have studied both Quenya and Sindarin a bit, and think I know only some things about these languages; but they can never be learned in the sense that one can learn German or Spanish, for two examples.

Good but why the one can't learn them as English or Spanish?

You can't learn any Elvish language in the sense of being able to speak it fluently [unlike English or Spanish]... Tolkien himself could not speak Quenya or Sindarin, nor was it his aim to have Sindarin or Quenya be spoken fluently by anyone.

It's all in the FAQ, and especially in more detail in the linked article Elvish as She Is Spoke.

I don't exactly "know" Elvish either, although I'd like to know how to speak many phrases. I just know 'I hate you' 'Farewell' 'Go kiss an Orc' and a few greetings