Ski Resorts establish ski trails and then classify those trails. They place coded signs pointing out the trails and the difficulty level of the trail. Here is your guide to reading ski trail signs!
However, determining which trails are suitable for you and your skills is a little more tricky than looking for the appropriate color and shape.
Beginning skiers should look for signs with the green circle:
The green circle indicates a beginner trail, suitable for the vast majority of skiers from beginners to experts. If you are new to skiing, warming up, or exploring a new resort consider staying on those trails marked by green circles (or on the trail maps by green lines) at least until you become comfortable with things.
One level up and we see:
The blue square indicates and intermediate trail. However, what is meant by intermediate? I find the blue square designation typically covers a wide range of appropriate skill levels. Some seem more like beginner runs and some seem out of bounds even for good intermediate skiers. Chances are if you can ski parallel you should handle most blues just fine and if you find yourself out of your league you should be able to come up with some way to safely extricate yourself and get back to the lift.
Up another notch:
Black diamond runs are for expert skiers. Now, maybe you come from Wisconsin or Ohio and ski black diamond runs all the time near home. Do not think this qualifies you to ski black diamond runs out west or out east. Think of the signs of grading the runs on a curve, where the most challenging runs at a resort are tagged as double black diamonds (the most difficult) and the easiest as green circles, so the black diamond run you ski in Ohio may actually qualify as a green circle in the Colorado Rockies.
If you do not know the types of trails the above marks do not even think of skiing runs marked by the double black diamond. These are the top of the pack in terms of difficulty
What makes a ski trail more difficult? A combination of factors. Namely the steepness of the run and the length of the steeps on the run. Blues and even greens may have some fairly steep sections but if they are short and followed by relatively flat stretches everyone should be able to maintain and regain control (if needed stay in control). In addition, whether or not the run is groomed or is full of moguls adds to the equation. Ungroomed runs and those with moguls are more difficult add in long steep stretches and you have a more challenging run.
Ski Resorts make an effort to mark their trails appropriately, but that does not remove responsibility from you to ski within your limits.