When writing with other people or bringing songs into a band context, there are several ways of sharing the credit.
Usually, credits are split 50-50 between music and lyrics. If you compose the music by yourself, but write the lyrics with someone else, you should get 75% of the credit of the song (50% for the music and 25% for the lyrics). The best thing to do is to come to an understanding before you write the songs. It's not always possible, but it can cause a lot of problems in the long run if you don't. I've seen the case of a band on the verge of signing a record deal. The guitarist was solely credited for the prominent track on the album although the lyrics and part of the music had been redone by the singer. During the negotiations stage, the guitarist “lent” the song to another rising singer. This caused such a feud between the guitarist and the singer that the band broke up instead of signing a contract. It wasn't too smart of the guitarist to do this, if you ask me. But that situation could have been avoided from the start.
You can always come to other agreements, as long as everyone is happy. If you look at most of the Beatles songs, you'll see “written by Lennon-McCartney”. The truth is that they co-wrote only about five percent of those songs. Lennon wrote about 15% by himself and McCartney wrote all the others by himself. They had agreed, from the start, to put both there names on all of their songs regardless of who wrote them in order to simplify matters and to put the good of the band ahead of everything else. It worked fine for them, they never had any disagreements over this.
The first thing you want to do is familiarize yourself with your country's copyright law. You don't need to study it for hours or learn it by heart, just get the gist of it. Then you'll want to look up other organizations that are in place to help songwriters.