[Just look at the music sheets, where copyright applies, every one of them states 'copyright'!
This invariably relates to the arrangement, i.e. the printed music, rather than to the original song. Along with that copyright notice will be the warnings about copying it.
Usually the payment for that sheet of music is sufficient 'payment' to the arranger. Sometimes, of course, the arranger may also be the composer.
If you played a recorded version of the original song, in its original form or variations of its original, you may need to pay royalties to whichever artist was playing/singing it.
For instance, The Floral Dance,
http://www.8notes.com/scores/611.asp
Founded on an old Cornish Air, but the famous one was arranged by Kate Moss. Therefore anyone else can do an arrangement of that original Cornish Air and sell it or give it away, as per the arranger in the link supplied.
It's advertised as Trad, because the author is/was unknown, but this arrangement by David Bruce is free, but you are still not allowed to photocopy it.
Kate Moss's arrangement is sold because it's such an excellent arrangement.
Another example: you can do your own arrangement of Mozart's Clarinet Concerto. therefore no royalties are payable and if you mark your version as Copyright, no-one else can use it without your permission, whether you sell it or give it way. By selling it or giving it away you implicitly give permission for it to be played.
Anyone else is free to do their own arrangement.
