There are many different chords, but the basic major and minor are probably the most frequently used, and also form the basis of many other chords.
Here are all 24 major and minor chords, each shown in their three inversions.
They are displayed on the treble clef staff, with keyboard diagrams to show how to play them, and in chord notation, as well as coming with audio files so you can hear what they should sound like.
In the keyboard diagrams below, the red dots show the three notes you should use to play the chord in root position. The green dots show first inversion, and the blue dots show second inversion.