It's not really a language you can learn in any conventional sense. You have to read, and re-read, and re-read what you've re-read. And then logically decode what it says.
Oh absolutely TC! I've studied it myself a bit actually. Very, very interesting to see how things have changed between then and now. It explains a lot of the peculiar things about English!
Linguistics has always fascinated me. I love it. In fact I have a site dedicated to (yes laugh now) the languages J.R.R. Tolkien created. I was impressed by how real he made them! Honestly quite amazing (though to be expected I suppose from a professor of Anglo-Saxon at Oxford).
The funny thing about Old English is seeing it in its written form. You can see where modern English evolved from it, but it's so darn German . . . speakers of both languages could pick it fairly quickly . . .
I don't speak Elvish per se . I'm personally more interested in the technical side. It's a bit like old english - you can't really learn to speak it; there are too many variables both internal (we don't have enough data to construct a full grammar) and external (the darn guy kep changing his mind at times!)