A picture of Mozart (even if appearing by chance in the sand) isn't in my definition of these abstract or modern art pieces that are confusing to me. I'm asking about the things that I have trouble recognizing as something worth looking at. Blobs and splatters of paint, or as shown elsewhere in the comments, a bag of garbage.
One way to think about art is that each piece is made at a point in time but is participating in a long din of conversation(s). If you don't understand the general arc of the conversation (or at least the conversation going on right around you), you will miss some of the aesthetic value of any piece. This is as true of Michelangelo as it is of Barnet Newman even if you have more context-free aesthetic/technical appreciation for Michelangelo's work.
Most museums also have docents which are usually more than happy to talk about various pieces.
What's hard to a appreciate is a semi-arranged pile of trash that's supposed to be a commentary on "disposable society". But which required little time or skill to create.
For example, you can look at an Impressionist painting, and most people would agree that by itself, it has some aesthetic value. Knowing the context of that painting might make it even more valuable, in other ways.
However, the pile of trash you mention does not hold any intrinsic value by most standards (you can find lots of those in any alley), but knowing the context, the commentary and the intention, makes it valuable.
Think of it like an inside joke.