There are basically only two shots in Curling, it's either "draw" or "takeout."
A takeout is supposed to remove your opponent's rocks from play. A draw positions your rock in play.
The simplest draw tries to put a stone into the house. An "open" draw is the first rock thrown into an empty house.
A guard is a draw thrown between the house and the hog line. It's a tactical move to either protect a stone already in the house, or just plain make it harder for someone else to score. It can be a center guard (on center) or a corner guard (off the center line). I mentioned the Free-Guard rule earlier, and I like it because it makes Curling more tactical.
A come-around curls past a rock and stops behind it. Usually you're throwing around a guard.
A raise taps a guard, moving it into the house, and a tap-back improves another shot.
A freeze places your rock directly in front of another stone -- very near, or in contact with it. Unlike a takeout, it doesn't move the other stone. Any attempt to take out a stone that is frozen against another stone simply transfers the impact to the stone behind it. The frozen stone stays put, and the other stone moves, probably quite a bit. If that other stone belongs to the other team, any attempt to remove your stone will likely remove theirs and not bother yours at all.
A Peel, a Normal takeout and a hack-weight takeout differ mainly in weight. Peel is hardest, and hack-weight is the lightest.
A Tick doesn't remove a rock from play, it just moves it a little.
I saved the Hit and Roll for last. In a sense, this has the best elements of a takeout, and the best elements of a draw. You take the opposing rock out, and leave your stone in the house. It's easy to find great Hit and Roll shots on YouTube -- this video from the 2010 WCF championship has two.
It isn't enough to have a strategy. You also have to make your shots.