OK Crayon. I'll start with my favorite.
(you realize that when discussing light the frequencies of waves are perceived as color and frequency is the number of waves passing a point during a specific time interval. Wave length is the distance that the wave peaks are separated. (Usually measured in nanometers). The wave lengths have differing characteristics. Think prism. Wave length and frequency are precisely related with electromagnetic waves as long as you don't mess around with gravity. Radio waves are measured in meters. (look at your short wave radio dial)
Imagine that you are in a boat in the middle of a river. There are wind generated waves in the river. Make it easy on us, make the waves go along the same path as the river.
Let the boat drift. Count the waves as they go by. (number of waves per unit of time) ie. frequency
Anchor the boat. Count the waves as they go by.
Put up the sail, go downwind. Count the waves.
Turn around and motor upwind. Count the waves.
Stand underneath a waterfall. Count the waves again.
Go downstream from a bridge. Have somebody drop a rock into the water.(Count etc.)
Go upstream from the bridge. Have the rock dropped and count again.
This with many more possible points of observation will illustrate both the Doppler effect and some relativity theory.
The main disadvantage with this analogy is that water waves move much more slowly than light waves or even sound waves.
When you realize that most, if not all, energy transfers utilize waves to transmit sound, light, vibrations, etc. that will get you started.
The Doppler effect is the logical outcome of a difference in relative motion between the observer and the emitter.
It also shows up as a difference in the speeds of time depending on your location. But that gets pretty deep into the nature of things and we are probably not ready to go there yet