E string Notes
F Bar chord
G Bar chord
A Bar chord
B Bar chord
C Bar chord
Bar Chords based on E open
These Bar chords are the first ones I learned to play, and I think that's true for just about everyone who plays guitar.
Just to refresh your memory, here's a picture of the E open chord.
E open chord
In this case it's the 6th string open E note
The chord name comes from the note that it is centered around, or Root note. This is the lowest note of the chord.
With the E open based Bar chords, the root note is on the 6th string at the place where the Bar is formed
Root notes on the 6th string
Between the natural notes, natural notes being E,F,G,A,B,C and D, are the Sharps and Flats. A note is sharp when it's a semitone higher, and flat when it's a semitone lower, so F# and Gb are the same note.

Just so I don't create any confusion, these notes are only called root notes as they relate to the E shape Bar chords.
For all other purposes, they're just notes on the E string.

Later on, we'll look at Bar chords based around the open A shape and the open C shape. The root notes for those chords can be found on the 5th or A string.
Some examples of E shaped Bar Chords
Bar Chords based on A open
A string Notes
B Bar chord based on the open A chord
With this particular bar chord fingering, although it's based on the A open chord, the way it's played is totally different from the standard A chord finger positions.
Instead of using the 2nd, 3rd and 4th fingers to press the notes other than the bar, it's a lot simpler to create a second bar to play the other notes by using the 3rd finger.

You'll notice that the 1st finger bar doesn't go all the way across the fretboard. This leaves the possibility open of accidentally playing the open E string.
To avoid this, I make the bar in such a way that the end of my 1st finger reaches over just far enough to automatically mute the 6th string, so it just makes a dull thud sound rather than sounding a note.
Here's the original Open A chord
In this case it's the 5th string open A note
The root note of this bar chord shape, like the E open bar chord shape, is on the fret that the 1st finger bar is formed. Only difference here is that it's on the 5th string.
The last chord is an octave up from the open A.
As you must've realised by now, the notes on the fretboard repeat themselves at the 12th fret, all an octave higher of course
Root notes on the 5th string
The root notes on the 5th string serve as a reference for both the A shaped bar chords, and the next set of bar chords, which are based on the open C chord.
I've left out the sharps and flats, but it's not rocket science to figure out where they are. In between A and B would be A# or Bb, between C and D would be C# or Db etc.

I'm sorry if I'm repeating myself, but I'd much rather over explain something than have people not understand.
Bar Chords based on C open
Here's the original Open C chord
In this case it's the 5th string note played here by the 3rd finger
The root note of this bar chord shape is the only one I can think of where the root is a note played by a finger other than the first finger, or barring finger.
Examples of C shaped Bar Chords
To play this shape of Bar Chord, I make a bar right across the first five strings, and use the tip of my first finger to mute the 6th string, the same as I did with the A shaped Bar Chords. I know there's only three strings that need to be barred in order to play this chord, but trust me, it's much easier doing all five strings.
Find the rest of the Bar chords
If you want, you can take any open chord and play bar chords using that shape - These definitely aren't the only ones to play.
If your fingers can get to the rest of the notes, while your first finger replaces the nut higher up the fretboard - It's a Bar Chord.

How to play Bar Chords | Barre Chords

Bar chords are based on the open chords, the only difference being that the nut of the guitar is replaced by the first finger, which forms a bar across the strings.
It takes a bit longer for the fingers to get used to playing Bar chords.

The best advice I can give on playing Bar chords is to try and make sure that your thumb is in the middle of the back of the guitar neck. This seems to help prevent the rest of the fingers from bunching up and not getting to the frets they're supposed to be behind.

Bar chords, correctly spelled Barre chords,
are also known as movable chords.
The reason being because you can hold one chord shape, like an E shaped Barre chord, and depending which fret the barre is played behind, you get a different chord.

Sliding up and down the fretboard and holding the same chord shape = Movable.
When you're pressing the Bar chord, pluck each note to hear if it's sounding correctly.
The first thing that most people have a problem with when playing Bar chords is with making the bar itself.

Just keep at it and in a few days, your fingers will fall into place naturally.
The Electric Guitar

How to tune the Guitar

How to use a Plectrum

Beginner Guitar Chords

How to play Barre Chords

How to play Power Chords

Guitar Scales

The C major scale on Guitar

The Pentatonic Scale on Guitar