Familiarize yourself with the components of the language. The Quenya dialect of Elvish has 5 vowels that are short: a, e, i, o and u and with those, there are 5 long versions: á, é, í, ó and ú. In addition, there are 6 diphthongs: ai, oi, ui, ae, eu and iu. There are 24 constituents: c, d, f, g, gw, h, hy, hw, l, ly, m, n, nw, ny, p, qu, r, ry, s, t, ty, v, y and w.
Understand the difference between short and long vowels. For example, á sounds like father, é sounds like air, i sounds like machine, ó sounds like sore and ú sounds like brute. The short versions sound very much like the longer versions, but more abrupt. Many of the dipthong pronunciations are self-explanatory, when used in context. Some examples are ai as in aisle and oi as in oil. Eu is less obvious; it sounds like so.
Memorize the differences in consonants. For example, qu is pronounced cw, c is always pronounced k, hw sounds like who, and ch changes depending on where in the word it is. At the beginning of a word it wounds more like an h, while at the end of the word ch has a throated sound very similar to Scottish. Many consonants have English pronunciations.
Stress the right syllable. The rules in Elvish are simple. If there is 1 syllable in a word, it is always stressed. If there are 2, than the first syllable is stressed. There is one exception to this rule: the word "ava," which means don't. Either syllable can be stressed in that word.
Take the time to listen to Elvish. The movies are a good resource, but you can also find many recordings of people speaking in Elvish online.