Minecraft – How to alternate redstone signal

Horizontal to horizontal (north to east, etc)
Use the same design, but put a redstone torch under the "hotspot" where the blocks will be pushed towards.

Horizontal to downward
Note that the input can be received from either opposing side (and you can move either the "red power line" or the "white receiver line" if you want to two "inputs" to come at 90 degree angles instead)

Horizontal to upward
Same as the above design, the input can be received from either opposing side (and you can move either the "red power line" or the "receiver line" (the one with the repeater) if you want to two "inputs" to come at 90 degree angles instead).

• The piston is a sticky piston.
• The repeater has to be set to 2 ticks.
• The glass block is required (but can be replaced by any transparent or non-solid, pushable block)
• The half-slabs are required (but can be of any material, or glowstone can be used instead)

As mentioned by @zzzzBov, what you are looking for is called falling edge detector. The wiki has a section on these, with multiple options to choose from, like these two:

On the left, the sticky piston retracts the diamond block, allowing a signal to go through before the repeater turns off. When the power is turned on, the diamond block cuts off the signal before the repeater turns on.

The design to the right works using locked repeaters. When you unpower the input, the repeater on the right is unlocked just briefly enough to allow a signal through. On powering the input, the repeater is locked before it can change state.

Another option you have is to use a rising edge detector, also known as a monostable circuit, and invert the input using a redstone torch. There's plenty of designs available online.