The A major seventh chord is commonly shown as the A7 guitar chord. It's pronounced "A seventh". The A7 chord uses only the five highest strings.
Notice in the diagram the A7 is played like an A chord, without the second finger.
Switch between A and A7, until both chords sound clear, and you have it memorized.
Next switch between the D and A7 chord, then between the E chord and A7.
When you play an A7, don't form it by forming an A chord, then lifting your finger out. Instead form the A7 chord directly, using only your first and third fingers.
After you have A7 well learned, practice switching between all the chords you've learned so far.
Remember, when you find a weak area, spend more time at it specifically. You must switch between all the chords easily!
The next chord is also easy to learn; the E major seventh chord.