The pronunciations given on this site are derived by applying the rules given
in Appendix E of the The Lord of the Rings, with Christopher Tolkien's 'Note on Pronunciation'
in The Silmarillion, and Tolkien's own comments in The Road Goes Ever On as secondary sources.
It's worth noting that Appendix E, taken alone, can be a little misleading: in the 'Vowels' section, particularly the note that the vowel i be pronounced as in machine (that is, as an 'ee' sound). Tolkien clarifies this point in The Road Goes Ever On where it's made clear that this 'ee' sound only applies to the long (accented) version of the letter. So, for example, the name Míriel would be pronounced 'meeriel'.