As wood dries it shrinks. As a result, it usually develops cracks, visible at the ends, which radiate out from the heartwood to the bark. Since the wood will often start to crack before it is completely dry, the presence of radial cracks is not a fool-proof sign that the wood is ready to burn. But, the total absence of such cracks is a good sign that it is not ready yet. The wood loses its sappy smell.
Dry wood is much less aromatic than green wood.
If you hit two pieces of seasoned wood together, they will make a resonant sound, like a bat hitting a baseball. If you have no other options, try splitting the wood into smaller pieces, mixing dry wood or kindling with it, and letting more air into the stove, so it burns a little hotter. The best way to dry your wood is to split it and then stack it so that it is well-ventilated, covered and off the ground. Storing wood this way for 4-6 months can make a big difference in the efficiency of your stove. Split wood has much more surface area than unsplit wood.