It is entirely possible to propagate an avocado from the seed - even from store bought fruit. What may be more difficult is getting it to produce fruit. Even if you are lucky enough to get to that stage the chances that it will produce a high quality, nice tasting fruit are not great. Many commercially grown avocado trees are propagated by means of grafting which ensures that the fruit stays true to type. In other words if the tree was grown from seed, not only could it take many years to mature and bear fruit but the seed may express genetic characteristics of another of its relatives instead of those that give the desired traits of that particular variety.
If you want to try (and I think it might be a nice experiment) what you have to do is to insert toothpicks into the seed so that you can prop it in a glass of water. Make sure it is the broader end of the seed that is submersed. I tried the toothpick method and also simply placing a seed in a cup of soil and only the one in water successfully germinated. Put the seed in a warm, shady or dark place and keep the water level topped up. The seed should sprout roots and a shoot which you can continue to nurture into a young tree. Plant the germinated seed in a large pot of good quality potting mix and place in a bright window. I have attached a timeline of pictures from my own attempt and full instructions can be found here:
I found that peeling the seed coat off of the seed helped the root emerge and also the larger Florida type avocado seeds worked better than the small Hass seeds. If you want to plant your young tree outside be sure to have a read of the avocado page here on PlantVillage and make sure you have the correct soil and climate where you are. Even if you don't manage to produce a fully fledged fruiting tree, you will have some fun and will at least have an interesting ornamental. I am keeping mine in a container for the time being as it will get too cold for the tree in the winter and I can bring it inside.
One seed in water one seed in water, one in soil 4/5/13
Beautiful young avocado plant 8/9/13
Root beginning to grow 5/5/13
Potted up and shoot beginning to emerge 6/6/13