A major

A7, A major and A minor are all somewhat similar to each other in terms of their form and their sound. Musicians describe them as being related because they share the same root tone, A. 

Let's start with A major. There are several ways to finger A major and here's a good one. Start by making an A7 chord. The index finger of your fretting hand is on the fourth string, second fret, and the middle finger of your fretting hand is on the second string, second fret.

We're going to give your index finger the job of holding down both the fourth and third strings  at the second fret, similar to what we did for an F chord. When you lay the pad of your index finger flat against those two strings, bend the joint closest to the tip of your index finger as far as it will go. You should be able to get both strings down at the second fret satisfactorily, and there ought to be room to for your middle finger to still be holding down the second string at the second fret. This fingering for an A chord is a good one to start out with, but the fingering you are most comfortable with is the one to use. 

As with all chords having the tone A as the root, begin your strum from the fifth string. See if you can get that first string to ring clearly, then try a chord changing exercise. You know the drill:

D    D    A    A

G    G    A    A

Here's another way to finger an A chord. Index finger on the fourth string, middle finger on the third string, ring finger on the second string. Squeeze 'em all in at the second fret. A variation of this is, middle finger on the fourth string, second fret, index finger on the third string, second fret, middle finger on the second string, second fret. Some find this fingering easier to manage.

Here's my favorite fingering for A major. Hold all three strings - fourth, third and second - down at the second fret with your index finger. A half-barre again. More difficult at first, but very valuable in the long run.

Which is the correct fingering? All of them. Our aim is to produce a collection of tones called A major. How you hold the strings down is up to you. Work first with the fingering that makes the most sense. Then work at the others. There may come a time when you will need them. There will come a time when each fingering will become easier to achieve.