Read the Lord of the Rings series by J.R.R. Tolkein. Without the actual experience of reading the series, your Elvish name won't have as much meaning.
Pick an Elvish name from one of the many elf characters in the book. Some of the most popular female names are Galadriel and Arwen.
Find Elvish name instant translators on the Internet. These websites instantly translate your own name into Elvish.
Look for an Elvish language lexicon. Because of the popularity of the Tolkein books, many authors have taken to writing lexicons of the Elvish language for others to read and understand.
Use the Elvish language lexicon to do your own Elvish name translation or look for one you like.
Research the meaning of your own name before trying to translate it into Elvish. As in other languages, certain Elvish names have certain meanings, and you'll want to find one as close to the meaning of your own name as you can.