*"Easy" as in "doesn't require advanced mathematics", not "easy" as in "any idiot with a pile of snow and a couple of brain cells to rub together could get one up in ten minutes"
I come from a place that elicits igloo jokes from people who aren't from there: Minnesota. "That's like the Arctic, right?" Uh, yeah. I'm going to sic my pet polar bear on you now.
I've gone ice climbing, hiked in the Boundary Waters in January, and slept outside in February. I've lived in Minnesota for 21.5 of my 23 years. Two of those years were in Duluth, Minnesota, on the north shore of Lake Superior - a city that a Surfing magazine article described as "remote and perpetually frozen", as if it were MacMurdo Station. Yet I have never slept in an igloo.
That said, I do know how to build them. There are five basic steps. Even if you have several people helping -the more people, the better- they will still take a while to complete.
1. Stomp. Stomp down a big circular area of snow. It helps to be wearing skis or snowshoes. This is the footprint of your future igloo. Then stomp down another big area- the quarry, if you will. The snow, by the way, should be at leat a foot deep, preferably much deeper, and packed firm. You might want to let the stomped areas harden for a few hours before moving on to step two.
2. Cut. Using a snow saw and a shovel, cut rectangular bricks out of the snow. Lots of bricks. Obviously, the bigger the bricks, the quicker the building process will go, but if you cut 'em too big they won't hold together very well. Do what works. If you have more than one person, this step can happen concurrently with step three.
3. Stack. The actual construction of the igloo is tricky to explain. You have to bevel the edges of each brick in such a way that the whole thing corkscrews upward, resulting in a sort of beehive shape. This diagram is helpful. Make sure it will be big enough to house all the people you're planning to cram into it. Pack any gaps between bricks with loose snow.
4. Enter. You need a way to get into your igloo. Cut a hole in the side, tunnel in from outside, or combine both as in the picture above.
5. Ventilate. Do not neglect this step. Using a stick, hiking pole, etc., poke airholes all the way through from the inside to the outside. Poke multiple holes in the top and on the sides until you're positive you won't get carbon dioxide poisoning in your sleep.
Viva la igloo!