How do I get better at endgames?

I can't give you general advice about the endgame, other than that you should study it.

in this particular endgame, where you are up a bishop, you should try to open the position up so your bishop and king can work. that means trading a few pawns.

with some pawns off the board, your king can penetrate into your opponents position instead of being stuck behind your own pawns.

you should also put your pawns on the OPPOSITE color of your own bishop, so that your bishop isn't blocked in, like what happened in the game.

if you do those things, you will win this endgame easily, even against stockfish.

@PurpleCherry here is that book: https://drive.google.com/file/d/1-C_gBR5j4J7ekHAx80nNgXgRB4l6_UP9/view?usp=drivesdk

@oberschlumpf I found these rules in book "Chess, a game of millions" (higher course) by Dragoslav Andrić and translated them from Serbian to English language and posted them here. Probably Fine meant that you should not use too much time to prepare secure advancement of the pawn but have that pawn as a tactical trump card where it could possibly force material gain in some way. And yes, preparing the advancement of the passed pawn beforehand is usually just correct, but you have to make sure that opponent can't prevent it's march (by a piece blockading the pawn that you can't kick away).

@oberschlumpf:

You have posted a tactical position about opposition. Strategic thumb rules often don't work in tactical positions.

I guess this "advance passed pawns as fast as possible" is a strategic rule like "develop towards the centre" or "don't move the same piece twice" when it comes to openings. A white pawn e. g. on the 7th row makes often constant pressure.

in general with learning anything,

first step is to understand
second step is to memorise
with chess, third step is to practice

Usually it's pointless to memorise without understanding, and that's true in chess, too, especially with end games where the exact position you get is likely to be one you've never seen before, so it's impossible to memorise moves.

With openings where the pieces start exactly the same it is possible to memorise moves without understanding why, but not only is it more interesting to understand the reasons why, you'll end up a better player.

this is coming from someone who has no interest in studying chess. but it's my current understanding of how to learn.

You had an easy win after 31 kxg1, the way to win was to get your king active via the dark squares and infiltrate the position. Pushing your kingside pawns onto dark squares and allowing him to play ...f6 to cover his weak squares is what dropped the draw. There may have still been a win even at the moment of your bishop sacrifice, but it would've been too difficult and technical to call a win if you're not comfortable in endgames.

One trick that I use to develop a plan in endgames, particularly in overwhelming endgames such as the one you originally enjoyed, is to ask myself the fastest way to win in the position if I had infinite moves. Since your bishop has no targets and your pawns can't achieve anything by advancing, it's easy to see that you earn the win by getting the king active.

After settling on a plan in this manner, you do the same for your opponent and see if he has a meaningful counterplan. This can give you a basic idea of how to proceed in a simple position.

I can tell you how I learned the little I know about endgames if that helps .... I had a beginner book of Reinfeld with a chapter on endgames and read & worked through that many times. I then bought a thin book that covered endgames comprehensively [in my case Keres' book] and worked thru that a few times. I then bought a bunch of thick books of Averbakh et al on specialized endgames and looked at specific topics in those as time permitted. In between I played through the games in "Capablanca's best endgames" and in "Endgame strategy" carefully making notes. When I was frustrated with my play I'd go back to the thin book and go thru the whole thing again. I think humans learn & store hierarchically: a few big picture ideas first, then the next level of refinement then the next. We retain what we revisit and reuse. I think for learning its better to study 3 books at 3 levels of detail than an endgame encyclopedia. (Of course encyclopedias are useful too just not for initial learning.) ... I also think a key is to convince yourself that you like endgames and so dont avoid them in games.