I am replacing a thermostat with a new Honeywell Programmable 5-1-1 model RTH7400D.
I have a red, green, white and blue wire currently. How should these be hooked up when they're asking for a red, green, white and yellow?

Do you have ac? If so its likely the blue wire is replacing the yellow wire that tstat is asking for.
Be sure to turn off power/breaker to furnace before replacing tstat