Oysters are available seasonally. The old rule for shellfish generally holds that any month (in the English language) containing the letter R is a good month for shellfish. (Note: this rule only works for the Northern hemisphere.) These are the colder winter months, and shellfish prefer cold water. More importantly, warmer waters mean an increase in bacteria levels, and the shellfish can be dangerous to eat.
Shop for a good oyster knife at a good kitchen supply store or at your local fish market. The features to look for are a thick, solid handle made of sturdy wood or plastic, a finger-guard (essential), and a short, thick blade. Strength and durability will be more important than sharpness or size.
Fresh oysters should be closed tight, and kept either in fresh sea water or on a bed of ice. Never select shellfish that are open! Store oysters on ice until ready to serve. Cover them with a wet towel or keep them in a closed container. An ice chest works well.
Look for the hinge of the shell. It should look like an exposed seam which wraps around a smooth corner. Insert the oyster knife into the seam, with the blade parallel to the seam. Use the point to do this, gently but firmly rocking the knife back and forth. Once the knife has been inserted, you can twist the blade to open the hinge a little more. Repeat this process, gradually inserting the oyster knife until you have cut the hinge completely.
Now slide the oyster knife along the inside edge between the shell and the meat. As you work at this step, try to keep the oyster level so that the liquid inside doesn't spill out. Some oyster eaters consider this liquid, or liquor, to be the finest part of the oyster-eating experience. There's one muscle, which looks like a thick cord, that holds the shell tightly together. Use the knife to cut this cord at the point where it adheres to the shell. This can be done in a sort of scraping motion with the knife angled against the shell.
Once the cord has been cut, the two halves of the shell should fall neatly apart. Discard the empty half-shell and place the full one on the serving platter.