How to tell if an abstract painting is "good"
If you've ever watched one of the cooking reality shows you know that there is good soups and bad soups. Same with chocolate cakes.
Guess what: even if Art is "an expression of your soul" and whatnot, there is still good Art and bad Art. It's subjective... up to a point.
Since abstract art is non-figurative, it can be hard to know what to look for. If I tell you "I painted a portrait or Ron Swanson" you can have a look and tell me whether it does indeed look like him, or not. But if I show you something called Untitled 21, you might just "not get it".
But don't let it intimidate you, here's a few things to watch out for:
Fine paintings will have a sophisticated palette. Maybe it's all black, or maybe it has hundreds of subtle colors; but they feel chosen and intentional. Very rarely will a good painting look like a unicorn puked a rainbow on a canvas. Also, like in makeup, a red is not just a red. Seek colors that vibrate and have depth, rather than something that could come in a basic crayola set.
Does the piece look like it's "trying to say something"? Painting is a tool to communicate. You know how even when you see a written language that you can't read, you can sense there is something being told? Same here. Seek out elements that feel like there is a consistent intention behind the piece. Tip: good painters tend to have details that come up over and over again, rather than reinvent themselves completely in every piece.
Like with people. as beautiful as a painting can be, ideally there is more than meets the eye. You are about to enter a relationship with this artwork, so it better have enough to keep you interested for a long time. This doesn't necessarily mean it should be "busy". I've seen minimalist abstract pieces that keep you interested with just a circle on them.
An abstract can be very static or full of movement, but it has to feel "balanced" (even if it's completely asymmetrical!). If it's boring, or flat, or dizzying, stay clear. Unicorn puke applies here, too.
At the end of the day, it's your choice. If you love something, go for it. It's your party and you'll buy it if you want to!