A copyright is a form of intellectual property law. It covers works of authorship, such as movies, songs, software, etc. A copyright protects the author from the moment the work of art (in this case, music) is created. In other words, if you compose a Psalm for a Sunday Mass, your work is copyrighted as soon as you complete it, whether you publish it or not. So, if someone else uses your Psalm, they should get your written permission to use the Psalm or you could bring a lawsuit against him/her for copyright infringement.
If someone publishes a piece of music, it usually becomes the property of the publisher. This means that you can no longer give permission to use the song (or other artistic matter). Anyone who wants to use it has to go through the publisher. The publisher then charges the user a certain amount and part of that amount will go to the composer. Whether you agree with it or not, this is how the composers earn their money, so it is very important that published music that you use is reported to whichever licensing company you use.
As soon as the piece is created, you cannot change the words or the music to a piece without written permission from the publisher or the author. When the Pope issued the moto proprio forbidding us to use Yahweh during Mass, the composer or publisher of Sing a New Song had to change the words to the song in order for us to use it during Mass. We couldn't legally change it ourselves without written permission from the publisher or the composer.
This brings me to another point. If you do want to change the words to a song for some reason, the publishers may handle it a little differently. Some may allow you to do it through them and some may have you contact the composer. In the event that you feel you need to change the words to a song, I would start with the publisher and they should be able to point you in the right direction. Remember that you need to get any changes to the music in writing. I would caution, however, not to be overly zealous about changes. In other words, don't call the publisher to change man to human or something like that. I believe the only time that we changed a piece of music was when we changed Dana Mangel's This is the Bread to This is the Body due to using it for Communion and it was felt that the emphasis should be on the body of Christ instead of the bread. You have to remember that this is the composer's "song of praise" and he or she wrote it from his or her point of view.