There are many good sources both to find synonyms for a word, and to understand what is the difference between the words.

Synonyms Dictionaries:

• Ludwig Ramshorn has written Dictionary of Latin Synonymes: For the Use of Schools and Private Students, which is now in the public domain. This is extensive dictionary that illustrate the difference between the words.
• Jean Baptiste Gardin Dumesnil’s Latin Synonyms: With Their Different Significations, close in style to Ramshorn’s book (and also in the public domain).
• Döderlein’s Hand-book of Latin Synonymes by Ludwig von Doederlein was transcibed by Project Gutenberg and available digitally for easy searching. The author of this blog, has developed a Twitter bot @LatinSynonyms that tweets periodically entries from this source for steady learning.
• De differentiis verborum by Popma is Latin-Latin dictionary now in a digital edtion. (also available in Latin-dict - see below)
• Gradus ad Parnassum contains synonyms for the words.

Digitally searchable:

• Latin-dict site allows the user to search several sources simultaneously (including Ramshorn, Dumesnil, and Popma (not completed)).
• Latinium’s site offers an interractive interface search by lemma of Döderlein’s Hand-book.