I have written lyrics to which I would like to have music put to. What's the safest and most advantageous way to copyright the lyrics?
If you are in the US, your lyrics were copyrighted the moment you put them on paper. (I can't speak for other countries.)
If you want to register your copyright in the US to make it easier to protect your rights, go to https://www.copyright.gov/ . They have instructions on doing it there.
To add to what Adam Stated, it is also important to have the lyrics dated. One of the first things we were taught when I was in engineering was to date all of our design plans in our notebook so that if someone where to bring us to court over copyright issues, you have at least more evidence in your favor that this was your original work and done before them. It would also be better to hand write because a date can be easily changed without notice on a word doc. On a piece of paper, there would be an erase mark or white out used in the date section which would raise speculation to the authenticity of the changed date (and with removal of the white out you can see the original date as it would leave an ink trace or lead trace even if it was erased). Not that this link provides how to copyright, but it may be an interesting read about what happens when a song goes to trial for copyright issues.