Which side is up? When you paint abstracts, how do you know which way to hang your painting? Here's how I do it. I only paint on square or rectangular surfaces. I've seen some nice circular paintings in this genre, but I've never done one. Though the same concepts apply regardless of the shape.
I like working with a 30" x 30" square wood panel. It's a big enough size to be substantial, but at the same time, it's still manageable. 24" x 36" horizontal is also a nice size. 30" x 40" is nice, but it's suddenly a much bigger deal to work with. What was within arm's reach, is now just out of reach.
When working with smaller pieces, I tend to prefer those as verticals. I think because they are small, they are typically used either as a grouping of paintings or to bring life into a smaller nook or space on a wall. So the less "wide," the better.
When working with larger pieces, I almost always do a horizontal. It's the opposite of how I approach the smaller paintings. You want something that commands attention in a room. You want to be able to visually move left to right in a sweeping motion. A vertical forces your eye into an uncomfortably narrow range of "top-to-bottom" viewing. Though, if you have a larger vertical space (without much room for whatever reasons on the left and right sides), a larger vertical painting will work. I'm only talking about abstracts right now. If you're painting portraits, obviously a vertical painting is often the best option.
It's usually pretty obvious to me which direction a painting should be positioned. You want a person to look to the upper left of the painting, similar to how you read a book. I look around and find what is the focal point of the painting, and position it so it lands in the upper half, left third of the painting. A focal point could be a lighter/brighter color zone, a distinct pattern or a play of colors. Generally, it's the most noticeable part of your painting.
If there isn't an obvious focal point, then follow the direction of the movement in the artwork. Shapes, lines, paint streams, color trails -- they force the eye to move through the artwork. If set up correctly, those streams of movement would ideally start in the upper left and move around the painting. This allows you to stand in front of the piece and view it for as long as you like, with the natural flow continually directing your eyes.
If you disregard visual clues like these, a viewer is apt to briefly look at your art and then their eyes will be directed off the painting and on to the next one. Or the previous painting, whichever way the eye is being directed. You want people engaged with the artwork, rather than being shown the exit at the entrance!