Question: We often seem to accept the idea that there were periods of time in which the entire surface of Earth was frozen, for the most part. This implies that there were periods of time in which the entire surface was NOT frozen over. Thus, there must have been heat and energy present on the surface. How did all that energy move to cause an ice age? It seems absurd for all that energy to just radiate into space or move deep into the Earth.

Answer: 
What's not been touched yet, and the current answers do cover a lot of ground, is the variability of solar input.  

Even IF the amount of energy radiated out by the earth remains the same (and it probably would, roughly), solar input is highly variable and is a major factor in determining the total energy budget of the planet.  

Even a small change can have far reaching consequences. Thus if the sun's output goes down by only a few percent (and that's well within its variability even over the 11 year sunspot cycle) temperatures on earth will swing with that (over that short a cycle that's pretty much averaged out by changes in ocean currents). If such a "dip" lasts longer, think a few centuries, you get a "little ice age" as we just emerged from in the 19th century (and by some accounts may be on the verge of slipping into the next, as the sun is again seemingly rather inactive).  

And the sun has longer cycles, such a low activity cycle lasting a few thousand years can well drop the earth into a full scale ice age. And as the ice sheets grow, reflection goes up, less energy heats the planet, less clouds form. Until the sun enters a high activity phase again, the planet will remain (relatively) cold.  

As said, this is unlikely to cause the entire planet to disappear under a blanket of ice. The last major ice age "only" came down to about the latitude of the Rhine delta in Europe for example.
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 I propose that the “snow ball Earth” was brought to a close by the dust from a huge meteorite (the largest known on Earth) impacting Australia (see <http://charles_w.tripod.com/antipode.html> ) settling onto the ice and melting it by a bare soil warming affect (see <http://charles_w.tripod.com/climate.html> ) and thus initiating the Cambrian. The dust fertilizing the ocean probably contributed considerably to the explosion of life then. That initiation was probably considerably assisted by the subsequent release of methane gas from methane ice under the ocean floor and by dust from volcanic eruptions from the Bahamas Islands, which are located at the antipode (opposite side of a sphere) of the above impact. The close correlation of volcanoes on Mars with meteorite impacts at their antipodes gives supporting evidence for such a phenomenon. 

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 Sincerely, Charles Weber