Suits are a complex garment, and it would take awhile to cover every single detail of their construction. However, here's a quick-and-dirty beginner's primer of the two most important construction considerations (not including style and fit, which depends on your unique) tastes and body type) to keep an eye out for when shopping for a good suit:
The Fabric
Suits come in a variety of fabrics, the most common being wool. Cotton, linen, and blends of these are also popular among lightweight spring and summer suits, but no matter what type of suit you're looking for, always avoid synthetic fabrics. Cheaper suits are generally made with these inferior materials to keep costs low. Suiting wools are typically marked as "super" followed by a number, referring to the size of the yarn, but don't get too caught up with this.
Synthetic fabrics like polyester are uncomfortable to wear — not least of all because they don't breathe — and they don't look good because they do not drape on your body as well as natural materials.
In contrast, a shell of a suit jacket made from quality natural fabrics will breathe, fit, and move better, making you look and feel better throughout the day. Even in warm weather, a light "tropical" wool weave can keep you cool in the heat, although cotton and linen blends are also ideal for this.
The Interlining
The interlining is the part of the jacket you don't see, as it rests between the shell and the lining. You will feel it, however, and it gives your jacket much of its shape and structure, so it's a vital consideration. The general rule of thumb here is to avoid glued interlinings. These are made from a material known as "fusible," which is heated and turns to glue, adhering the shell to the lining. These are stiff, don't breathe, don't drape well, and can even come loose and start to form air bubbles over time.
Instead, get a suit with a free-floating canvas or half-canvas interlining. These are made from natural fibers like horsehair, making them more breathable and comfortable to wear while giving the jacket a nice drape and the lapel a rolled appearance.
An increasing number of mid-range suits are half-canvassed, meaning that the chest and lapels of the jacket are canvassed. Canvassing requires more handiwork to make, so it's naturally more expensive than a glued suit, but remember: A suit is more than a purchase, it's an investment.