We are sending a simple signal from a transmitter to a receiver connected to one of our analog inputs to our Arduino Micro. We have a the signal being read and converted into samples. How can we go about coding the Arduino to make it recognize our signal?
Those kinds of devices work great with the VirtualWire library - does the transmitter have a microcontroller with it also?
Otherwise, you are stuck just reading a digital pin, and guessing as to when digitalReads of that pin are to have any meaning.
We are trying to make a key fob for the transmitter so no, it won't be controlled by another microcontroller. Our transmitter circuit is sending a constant square wave signal using a TTL chip and some resisters and diodes. This gives us about a 50% duty cycle on the transmitter data pin.
My group and I are new to microcontrollers, and we will look into that library you suggested and hope to find a feasible way to recognize the rf square wave sampled signal that we have so far. Thanks! 
Just use a pair of these chips , SC2262 encoder, SC2272 decoder and connect the output of the decoder to the Arduino.
Does all the hard work for you.
SC2262 are specifically designed for small transmitters like key fobs.