Typically, a lyric writer will be a freelance writer who submits their work to composers, record companies, or performers who are looking for words to put to the pieces of music they have written. It is not uncommon for a lyricist to have a musical recording submitted to him or her, and be asked to put together words to go along with it.
It is important that a good lyric writer be able to work well with other people. Often, the work of a lyricist is scrutinized and edited in order to come up with a finished product. Communication and people skills are a must if you are going to be working with other composers or writers.
Sometimes a good lyricist is able to not only write the words to a song, but write the musical aspect as well, and perform it on their own. Some very successful artists and entertainers have mastered each aspect of song writing, and have gained wealth and notoriety because of it. Some excellent examples of this would be John Lennon, Fiona Apple, John Mayer, Elton John, and Jack Johnson (just to name a few).