Hi Vjah,
What about starting simple:
1. Rule of Thirds - focal point (center of interest) in one of the sweet spot
2. Mostly x, some y, and little of z (where x,y,z could refer to tonal value, contrast, color, etc.)
3. Watch the edges of the painting... nothing to draw the eyes outside the frame; watch how the picture is cropped. Nolan explains this well in one of his lessons on composition, how the eyes should flow inside the painting along a loop (like a circle of a triangle).
Also:
Greg Albert wrote a simple book where he describes the various applications of only one rule 'Never make any two intervals the same'. Interval is defined as all the different elements of composition. It is presented very simply (likely oversimplify for the accomplished artist), but it is a nice starting point for beginner; then all rules can be broken right? What is called, artistic licence? But, I think it could be used to identify problems when 'something doesn't look right'.
The reference is: The simple secret to better painting, Greg Albert. ISBN-13: 978-1-58180-256-6. Not a cheap book ($25US, $30Can), but I got in on loan at our public library. It was very helpful for me to start looking at a way to balance a painting to make it nice, it also gave a lot of examples of bad composition.
Cheers, Annie