A very, very basic primer:
Construction quality is the key. Best-quality suits have a "floating" canvas inside the jacket, to give the coat its shape and help it mold to the body. Lesser suits are fused, meaning they are held together with a glue-like fusible. Poor quality suits feel stiff and hard because of this fusing, which can even "bubble" and render the suit fit only for the trash bin. In between you'll find suits that combine fusing and canvas. A suit might have canvas lapels, for example, to give the lapels a more attractive "roll." Not all fused suits are bad -- some can be very decent -- but full canvassing is a prerequisite for a truly exceptional suit.
To tell if a jacket is fully canvassed, pinch the fabric below the bottom buttonhole on the inside and outside. Gently pull the cloth apart. Can you feel a third layer inside? The layer in the middle is the canvassing. It won't be there on a fused suit.
A few other things to look for: Top-quality suits are expensive partly because they contain a good amount of handwork. The armhole inside the jacket, for example, will be handsewn -- look for small sewing irregularities instead of the smooth regularity of machine stitching. You won't find this on low-end department store models. The more handwork, the more expensive the suit.
Also, feel the fabric. Does it have a nice hand? Does it feel soft and smooth to the touch? Cheap suits use cheap cloth, and it's very easy to tell the difference once you've handled a few of each.
Check the lapels. Good suits have beautiful lapels that roll gently to the buttons. Cheap suits usually have lapels that are pressed flat, so that they form a hard "V". Similarly, nicer suits have nicer buttons. Are the buttons obviously a single-color plastic? Bad sign.
Look inside the trousers. How does the stitching look? Is it nicely finished or ragged? Is there extra material to let the waist out? Good trousers will have a "split" in the middle of the back of the waistband, to facilitate alterations.
Finally, try the coat on. Does it feel good? Does the chest feel soft? Does the jacket move well with your body? Fused coats once were known for being stiff and unpleasant, but they don't need to be these days. At the very least, any decent suit will feel good to wear.
Hope that's helpful, and not more info than you wanted.