When playing guitar chords there are two basic types:

Open chords (chords which contain an open string or strings)

Open strings are strings that are played with the chords but not fingered with the left hand. Assuming the player is right-handed.

Movable Chords (Chords which do not contain open strings)

Moveable chords move up and down the fingerboard while maintaining their chord type.

When playing Open chords, the chording hand thumb is generally over the neck of the guitar while using good pressure from the fingertips against the fingerboard while maintaining an arc on the fingers to not mute any adjacent strings.

When playing moveable chords, the fingers of the chording hand generally continue to apply pressure with fingertips while maintaining an arc on the fingers. The thumb however is generally behind the neck as opposed to over the neck. Depending on the chord sometimes a "Barre" will be required. This is when a finger of the chording hand lays flat across two or more strings.

Happy Chording!

Jay