Start by bringing a pot of water to a low boil. Use a wire strainer or large slotted spoon to lower tomatoes into the hot water so you don't burn yourself. Add just as many as will fit, allowing all of the fruit to be submerged.
Leave tomatoes in the simmering water for 30 to 60 seconds, or until the skins appear to be wrinkling slightly.
Use the wire strainer again to lift the hot tomatoes out of the pot and transfer them to a sink or bowl of ice water.
Allow tomatoes to sit for another 30 seconds or so. You'll see the skin begin to visibly fall off of the flesh.
Remove each tomato from the water individually and use your hands to slip the skin right off the fruit.
If you have more tomatoes to skin, repeat the process.
Notes
Have you ever frozen whole tomatoes? Yep! You can do that! And a funny thing happens when you do. When you remove the frozen orbs from the freezer and allow them to come to room temperature, the skin just slips right off. You can hasten this by dropping the frozen tomatoes in a sink full of room temperature water. That makes two easy methods for peeling tomatoes!