1. Wood or not? First identify if the piece you are looking at is made of hard wood or a wood composite that has been veneered to look like wood. You can do this by looking at the edges. Often when using composite, they cover all sides with long grain veneer. You can check by carefully looking at the wood grain, does it match on the top and the side? Are they continuous? Can you see the end grain?
2. Look at the joints. The joinery can tell you a lot about the quality of the piece you are looking at. In general terms, the less hardware, screws, nuts, bolts, etc. you see, the better. The highest quality pieces will use traditional woodworking joinery such as mortise and tenon or dove tail joints. These should be precise, with no wood filler and no glue spilling out of the crevices. You can easily check the joints by taking a look at the underside, the inside, and the back of the piece.
3. Back and bottom. If you don´t have access to the bottom or back side of a piece, I have also found that checking the front, sides and bottoms of drawers can give you a pretty good indication of the overall quality of the piece. Are the sides and front connected with joinery or are they just nailed or stapled together? Tap the bottom panel a few times, feel its strength. Solid wood or sturdy plywood are ideal. If you see a very flimsy board or something that looks or feels like cardboard, you should be wary.
4. Is it sturdy? What is the overall strength of the piece? Are the legs sturdy or are they a bit shaky? Will it be even shakier when it's full or when someone sits on it?
5. The devil is in the details. Do the drawers fit perfectly into their slots? Is it difficult to move them in and out? Are all the surfaces smooth and sanded? Including the interior surfaces of drawers?
6. Finish. Is it smooth and even? Is it splotchy or does it have areas that are thicker or darker? Does it feel like plastic or is it sticky?
7. Hardware. And finally, take a look at the hardware. Are the hinges good quality? Do they open and close smoothly?