Music is about the relationship between notes and chords.
Songs are written in a key and the associated scale.
Example Key of G major
Notes in scale G A B C D E F#
Some 3 finger open chords
avaliable from within this scale G Am C D Em
This means you can use any some or all of these chords for a song written in the key of G
In short the chords will work together as they are from the same scale.
Note
Go to the "Chord Chart" page for an illustration of selected simple chords from major scales