Minecraft wiki entry for Logic, associated text: Behavior (i.e., how it works): An instant inverter has two functional elements, and a piston, or pistons, that activate them:
a constant power source with output that can be instantly powered off (but powering it on takes time): either a redstone block that ceases to provide power as soon as piston starts moving it (within the same tick the piston receives or loses power) or a solid block in front of a powered repeater or comparator, powering redstone dust; as soon as the block starts moving the dust is unpowered.
a signal line with output that can be instantly powered on but not necessarily off, its input delayed by and sustained for 2 ticks. The "instant on" is achieved by the dust-cut technique: a solid block placed against edge of a block over which a redstone line is running, disconnects that line from line below. Start of motion of that block instantly reconnects the line and provides power. The delay is achieved by running the input through a 2 tick repeater, two torches or similar means. That means, when power appears on input, the block moved by piston is able to cut the line before signal passes through the delay. With input unpowered, the output is instantly activated and the line still provides power "stored" in the repeater for two ticks, which time is sufficient to reactivate the constant power source from previous point.
Piston, or pistons, to move the block/blocks activating the elements from point 1 or 2.