The basic knot for the beginner to learn would be the four-in-hand knot. This is the simplest knot to tie. If you master this knot, you will be prepared for most semi-formal events.
Button your collar at the neck. Fold it up so you can slip the tie around your neck. This helps you tie it in the right spot the first time, and helps prevent wrinkling and stretching the tie fabric.
Adjust the length of the tie. Some people prefer the ends to be exactly the same length after you've finished tying it. Unfortunately, ties usually come in one size only, so it's hard to say where the ends will meet up. You don't want a tie that only hangs to the belly-button or one that hangs over your pants fly. The tip of the broad end should extend just to the top of your belt buckle.
There is a good general rule to follow to get the right length. To begin, drape the necktie around your collar so that the seam of the tie is lying along the collar. The broad end should be on the side of your dominant hand. If you are left-handed, the broad end should be on your left side, if right-handed on the right side. To measure it, place the tip of the narrow end just above the fourth button down your shirt (the one above your navel), and eliminate the slack by pulling down on the broad end. The tie seam should remain hidden in the back.
To tie your tie, first grab the narrow end about three inches down from your neck with your non-dominant hand. This is the spot where you will make the knot. Take the broad end with your dominant hand and pass it across and over the spot, holding it there with your non-dominant hand.
Bring the broad end around behind the spot, then around and over again. Then pull the broad end behind the spot and up through the "V" at the top.
Let the broad end flop over and hang down. Now tuck it between the top wrap of the tie and the place you have been holding. Use both hands to straighten the knot and pull it tight.
Pull the knot gently but firmly. Look at the tie in a mirror. Is it straight? Does the broad end hang down too far, or not far enough? Loosen the tie if necessary, and readjust the length of the narrow end as needed so that your tie will be the proper length after the knot has been tightened. The Four-in-hand knot will be slightly larger on one side than the other. The knot should be smoothly wrapped, not wrinkled or folded over on itself. If you need to, take a moment to fuss with the knot so that it looks even and the rest of the tie hangs down straight. The last step is to turn your collar down.
With practice, the four-in-hand knot is very easy to learn and a very good looking knot. This should serve you for most circumstances.