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.
One cause of glaciation on earth is dust from volcanic activities ie you have heard the term volcanic or nuclear winter.

During glaciation continental plates with a mile or two of ice piled upon them increase vastly in weight and actually sink. When we see a rock we see a hard stone object, but that rock within the earth under a vast amount of pressure is not "rock" solid, it is more the like peanut butter, it is soft and pliable. This is how continental plates are able to sink under the weight of a mile or two thick sheet of ice.

Not only do the continental plates have weight pushing down on this peanut butter like rock beneath us, the oceans also have weight and they as well push the plates beneath them down into this peanut butter like stone.

During glacial maximums ocean levels drop by as much as 400 feet, so what is currently 400 feet underwater was dry land during the last glacial maximum. This loss of 400 feet of water across all the oceans of the earth greatly reduces weight upon the ocean floors. That same water is turned to snow and collects as ice on the continental plates this adds that same weight now to the continental plates. So the oceanic plates raise while the continental plates drop.

During interglacial periods you get a lightening of continental plates and the oceanic plates become heavier with the return of high ocean water levels ie global sea level rise such as we are experiencing currently. Continental plates rise and oceanic plates drop. This reaction is not immediate, again if you imagine peanut butter if you put a board over several inches of peanut butter and add weight to the board it takes some time for the peanut butter to squish out the sides, the same with the continental plates and the soft stone they sit atop of. It takes thousands of years for the continental plates to rebound to their original height. During this rebounding of the continental plates and the dropping of the oceanic plates volcanic activity slowly starts to increase. Eventually it is only a matter of time before you get another great volcanic eruption due the plate movement that produces a great deal of ash in the atmosphere, this continues again and again with increased levels of volcanic activity. This ash reflects light back into space before it is able to reach and warm the surface, thereby reducing average global temperatures. 

This is certainly not the only mechanism that controls glacial maximum and interglacial periods but it does work in concert with the afore written answers to your question. The normal condition for our planet during human existence is glacial maximum conditions, what we are experiencing now an "interglacial" period exists only about 20% of the time somewhere on average of about 20k years per 100k years. This is the second interglacial period in the last 100k years. You have go back to 120k to 130k years for the next previous interglacial period.