For the last 7-8 years I've been in Nashville, Microsoft Word has been my go-to for typing and organizing my lyrics.
Here's an example of how I structure a lyric:
SONG TITLE DATE OF CREATION
I use all-caps because it's cleaner and less confusing than trying to figure out which letters should be capitalized. During my college internship at EMI and when I did some temp-work for Universal Music I learned that this practice is pretty standard.
In order to keep the song on one page, I use the tab function to set the chorus apart and only type it once (some people put the chorus in bold instead). The bridge (if there is one) is offset twice as far.
Of course, this style of typing only works for songs that fit this common song structure, so however you type your lyric should be determined by how the song should be written first.
Here's the lyric Melinda Schneider and myself wrote that Olivia Newton-John ended up singing:
Once you have written songs with multiple people, it's important to keep things organized. I have an overall folder entitled "lyrics" with sub-folders labeled with co-writers' names. Within each co-writer's folder, I have every song we've written.
One thing I'm interested in is the potential for Google Documents. It boasts many of the features of Word, but allows you to access your documents anywhere you can get Internet access.
Keep writing (and typing),