The A chord on the guitar is one of the easier chords to play. It can be played several ways, the most common is at the 2nd fret in the open position on the guitar.
Here is the A chord on guitar in open position. It is played by placing your first finger on the 4th string second fret, second finger on the 3rd string second fret, and third finger on the 2nd string second fret. Avoid hitting the low e string when strumming, and let the 5th string (open A) and first string (e) ring. If that sounds confusing, take a look at the chord chart below. If you are lazy like me, you can play this chord with your first finger barred across the 3 strings.
Here is another variation of the A chord that is played as a bar chord on the 5th fret. You'll find it sounds mostly the same as the open A chord position, but with a little bit different sound. This version of A is played by barring across the 5th fret with your first finger, 3rd finger on the 5th string 7th fret, 4th finger on the 4th strong 7th fret, and 2nd finger on the 3rd string 6th fret.
Here is a chord diagram. Try substituting this one in for the open A chord for extra practice.
Similar to the version above, this is an A chord without the bass notes. Try experimenting with this one when you just want to color in the sound a little bit and not bring in such a full sound. It is played by barring the 1st and 2nd string on the 5th fret, 2nd finger 6th fret 3rd string, and 3rd finger 7th fret 4th string.
Way up at the 12th fret is where you will find this A chord variation. It is played by barring the 1st through 5th string with your 1st finger, then barring the 2nd, 3rd, and 4th string with your 3rd finger. The diagram says to use 2, 3, and 4, which you could do, but most players just bar it with the 3rd finger.