Some of the chord forms just shown can be difficult to play, particularly the G form. The most important thing is to be able to visualize these shapes, especially the positions of the root notes. Remember that major chords are made up of three different notes. Any more notes in a chord shape are just doublings of those notes.
This means it is possible to play just three notes from any of these chord forms instead of using the whole shape. Some common examples of three note voicings on the 1st, 2nd and 3rd strings are shown in the following diagram, along with an example which makes use of them. Once you have learned them, try transposing them to other keys by moving them up and down the fretboard.
The term half bar means the first finger is barring some strings, but not all six. The first G chord shape shown is played with the first finger barring the 1st and 2nd strings. The second G chord shape is played with the first finger barring the 1st, 2nd and 3rd strings. Practice playing them separately until you can sound all the notes clearly. Then play the following example which uses these shapes to play the chords G, C and D.