Copyrights
A songwriter has a copyright the second he records his song or writes it down. However, in order to prove you created the composition it is important to register the music with the copyright office.
A "PA" (Performing Arts) registration protects the song. An "SR" (Sound Recording) registration protects the recording. Typically on a commercially released album the label owns the SR copyright, while the writer or his publishing company owns the PA copyright.
Publishing
In addition to artist royalties a record company pays a publishing royalty ("mechanicals") for each record sold. The current statutory rate is 9.1¢ per song per album sold. If the writer is also the Artist this is considered a "controlled composition". Often an Artist will be asked to accept a lower rate for controlled compositions by the record company. This royalty is paid by the record company.
The writer also receives a public performance royalty for every time it is performed (i.e., radio, nightclubs, etc). Every time your music is played on the radio you are entitled to performance license money. Each writer joins BMI or ASCAP which collects and distributes these royalties to their member writer/publishers.