Here is a video of it working:
In order to store the IR signal, you need to turn a switch on and feed the microcontroller the IR signal you want it to remember. The green light means it recognized the stored signal. In the video above, I had the receiver circuit set to receive the 1 button, and changed it to wait for the 2 button to be pressed.
Further improvements I plan to make are: to scale down its size, to make it more reliable, and design a board layout for it.
With this circuit completed I can finally start making remote controlled robots and other cool electronic devices.