If you find the bar chord challenging, you're in good company. With just a few simple tips, you'll be well on your way to sticking the landing of that bar chord. First, it helps to know why the heck you should take the time to master it:
Why learn the bar chord in the first place?
Because so many great songs use bar chords! You'll really shut the door on your ability to freely range among your favorite tunes if you can't make a bar chord. The main one we're working towards is the B chord and its variations (B, Bm, B7, Bm7). Do you want to play the blues? If you're aiming at the classics in the key of E, you're going to need a B or Bb. Got a favorite song in the key of F? You'll likely need that B. Go ahead, it's worth it!
Your step-by-step guide to making a ukulele bar chord
The key here is to use the side of your finger, not the flat, grip side. I come at it with a reverse karate chop, slowly shifting my hand so that the thumb side of the index finger lays across all 4 strings in the space between the first and second frets. As with all other chords, do not touch the frets themselves.
Make sure that big first knuckle of your index finger is up on the fretboard. The reason for this is that the knuckle is what makes that finger flatten out, driving it into the strings. If you think of it as where you would put a C-clamp to flatten a piece of wood, you'll get the idea of how to use that knuckle effectively.
Your fingertip will likely hang well over the top edge of your fretboard.
Don't try to flatten your finger by bending your fingertip -- that just increases the amount of finger that is NOT touching a string. It's all about flattening the entire finger through that first knuckle.
The tip of your thumb should be pressing into the back of the neck, directly behind that exhausted knuckle of your index finger.
Double-check that you're still pressing with the SIDE of your index finger!
Notice how, when you crank your elbow in towards your rib, your index finger becomes more parallel with the frets? Use that crank to help deliver that finger to exactly where you want it.
Keep breathing!
With only your index finger making the bar at the second fret, you're making a Bm7 chord, which is used quite a lot.
It can help to slam your middle finger down on the index if you need some extra torque to get a sweet ring from all 4 strings.
Pluck each string - are they each ringing out? If not, readjust.
Don't overdo it at first!
To move on to making a full B chord, while you've got that index finger in place on the 2nd fret, place your middle finger on the C string on the first fret below your bar finger (which is actually the third fret from the top), and your ring finger on the G string on the 2nd fret below your bar finger (the fourth actual fret).
All of this effort goes towards bringing the A chord shape down towards the sound hole, by 2 frets. Because you need your index finger to make the bar, you have to use the next two fingers to make that A chord shape under the barring index finger to form the B.
Similarly, to make the B7, you're making an A7 at the 3rd fret space with your middle finger, UNDER the finger bar. To make the Bm, you're making the Am at the 4th fret space with your ring finger, UNDER the finger bar.
As with everything else about playing the ukulele, there are many ways to go about making the bar chord. The above steps are what I learned and have found to be effective not only for myself but for teaching others.
That said, some people opt to make the B chord by barring only the E and A strings at the 2nd fret, with the middle finger no the 3rd fret of the C string and the ring finger at the 4th fret of the G string. I'm not a fan of this technique, as it doesn't address the need for a full bar when making the B7. But whatever works for you to get you to and from any one chord to another in time and on beat AND with a smile on your face, go for it!
Keep at it! Use your stubbornness to help you stick to it until it comes -- it will! It took me a while to get it down, and the persistence really paid off. Go ahead and give yourself the gift of kicking your skills up a notch by getting that B down.