Place the tomato on its side on a work surface. Hold it still with one hand and insert the tip of a paring knife about an inch into the fruit, at an angle just outside the core. Move the paring knife with a sawing motion and rotate the tomato toward you until the core is cut free.
Pierce the tomato at the stem with the apple corer, give it a twist, and remove the core.
Place no more than five cored tomatoes in boiling water. Boil them until the skins split and begin to curl around the cored area, about 15 seconds for very ripe tomatoes of up to 30 seconds for firmer, underripe ones. Take the tomatoes out of the water with a slotted spoon and place them in a bowl of ice water to stop the cooking process and to cool them. Then, with a paring knife, peel the skins using the curled edges at the core as the starting point.
Core the tomato using one of the tips above, then use a paring knife to take off a strip of skin from the exposed core area down to the blossom end of the tomato. Slice the tomato along the skinned strip so that the knife doesn’t have to cut through skin (the hardest part to get through) before it enters the tomato.
To seed a round tomato, core it then cut it in half along the equator. If the tomato is ripe and juicy, give it a squeeze and shake out the seeds and gelatinous material. If it’s not ripe, scoop the seeds out with your fingers or a small spoon. To seed an oblong tomato, cut it in half lengthwise through the cored end. Cut through the inner membrane with a paring knife or break through it with your finger and then scoop out the seeds and gelatinous material.
Like these? See more quick tips at Cook's Illustrated.