You should already have some idea how to form barre shapes, but let's go over the most commonly used shapes!
Here are the Major, Minor, and Dominant shapes for what we call the E shape. Make sure to note that this does NOT mean it's an E chord. We call this an E shape barre chord because it borrows the structure of the open E chords.
You can move your root note anywhere on the low E string to use the shapes to produce chords of all 12 root notes. With three shapes to work with, that's 36 chords in total!
As you can see, some intervals are repeated to provide a larger sound. You can absolutely omit some of the notes as long as you still have a root, a 3rd, a 5th, and for the Dominant chord, a 7th. In some cases we can reduce even further, but that's getting into Building a Chord territory.
Major E Shape
Minor E Shape
Dominant E Shape
Here are the Major, Minor, and Dominant shapes for the A Shape. Like the E Shape, we call it that because it borrows the structure we used for the open A Chords.
You might wonder why we need to know these shapes when they're making the exact same type of chord as the E shapes were, but it's always good to have options! It's also often much simpler to swap to an A shape than to jump up a whole bunch of frets to play the entire song with E shapes.
Lastly, this will all come back into play in the future as we see what else we can do with these shapes, so it's a good idea to learn them now.
Here's a question for you. What happens if we barre the low E string as well? What interval is being played?
Major A Shape
Minor A Shape
Dominant A Shape
If you've got the basic idea, try a few chord progressions using these shapes exclusively. If you need suggestions, you can try these:
F - Bb - C7 - F
G - D - Em - C
Cm - F7 - A# - Gm
Working these out, you might notice that you've got a higher and lower option for playing some of these chords. Neither are right or wrong, they're both valid ways of playing the chords, and they can apply a different feeling to the song! This will be something to keep in mind for the future - using this to your advantage will take you far.
Once you've got these shapes down, you'll have at least two ways to play all of the Major, Minor, and Dominant chords - and a third option for many of them thanks to the open shapes we learned previously. Nice!
You really can't get too good at these shapes. They'll show up in some capacity in almost any popular genre of music. Don't worry if they seem difficult now, it's just that you're asking your hand to do something new. A little daily practice will have these barre shapes beat.