For me, for modern/abstract stuff at least, it took a lot of looking at it and not getting it, but being around people who were into it. Now I describe the experience as almost meditative/introspective: I look at the art, let it fill my field of view, try to change how I'm looking at it (especially for things with any kind of 3D effect/visual cues, closing one eye can make a huge change), and just kind of introspect.
But also, different people like different things. I would echo others and say go see some design, some formalistic old-masters stuff, some photography, some decorative arts, some sculpture, some theater, some street art, some Burner stuff, the list goes on.
For some people, provenance and the story of how something was made is a huge part of the art; some people don't care much at all. So you might try learning some history; maybe read a book about Basquiat, listen to a podcast about Picasso, or a documentary about Dali. Then go see the art. My personal aesthetic does not run into the caring-about-the-story-behind-the-art very much, but I do get it a little bit -- I saw an exhibit of Warhol photographs of famous people at the Whitney recently and, while the photographs are fine technically, what really makes the experience is imagining the very-different-to-mine life that Warhol must have been living to be running in these circles; it's almost a nice way to let oneself daydream about being famous.
Finally, avoid any normative thoughts that you should like art (or a particular kind of art); not only is this nonsense, it's likely to make it harder to appreciate the art, rather than easier!
I've been interested for awhile in a distinction between math and philosophy here. Just descriptively speaking, we don't tend to teach math from original source (at least, not well-established math like you'd see in high school and early college). We don't teach calculus out of Newton/Leibniz/Cauchy/etc, we don't teach Fourier analysis out of Fourier, etc. Maybe geometry students will work from the Elements, but I certainly didn't.
But in philosophy, students do read everyone from Plato to Rawls in the original. There are (lots of) supplementary texts, of course, but they're companions.
I think that shows an interesting divide that the way we actually think about philosophy is not just a catalogue of arguments and positions one could take, but that the famous works are things worth reading unto themselves. There are a few math papers like that ("God Created the Integers" tries to anthologize them) but they are the exception rather than the rule.
But also, different people like different things. I would echo others and say go see some design, some formalistic old-masters stuff, some photography, some decorative arts, some sculpture, some theater, some street art, some Burner stuff, the list goes on.
For some people, provenance and the story of how something was made is a huge part of the art; some people don't care much at all. So you might try learning some history; maybe read a book about Basquiat, listen to a podcast about Picasso, or a documentary about Dali. Then go see the art. My personal aesthetic does not run into the caring-about-the-story-behind-the-art very much, but I do get it a little bit -- I saw an exhibit of Warhol photographs of famous people at the Whitney recently and, while the photographs are fine technically, what really makes the experience is imagining the very-different-to-mine life that Warhol must have been living to be running in these circles; it's almost a nice way to let oneself daydream about being famous.
I saw, but have not yet listened to, an NPR Life Kit podcast about this topic: https://www.npr.org/2023/01/05/1147239071/dont-get-art-you-m... . Generally I like Life Kit although it can be hit or miss. So maybe some inspiration can be had there.
Finally, avoid any normative thoughts that you should like art (or a particular kind of art); not only is this nonsense, it's likely to make it harder to appreciate the art, rather than easier!