While tie clips are not obligatory, they can jazz up an otherwise-ordinary suit. As with all accessories, though, it is important that you wear your tie clip correctly. Wearing a fashion accessory incorrectly does more damage to your outfit than not wearing it at all would, so follow a few key points and wear your tie clip with pride.
Tie clips are not often worn. This means that their presence will attract attention on their own. More importantly, though, this means that you should keep your tie clip simple. Don't be seduced by a "wacky" or "zany" tie clip; you'll just attract overt attention and you won't put forth the sophistication you were trying for.
Ridged vs. Smooth
A tie clip has a ridged end and a smooth end. Always, always make sure the ridged end is on the back. This is the end that holds the tie clip together, but it is not the end that you want to present to the world. It is key that you do this correctly. Otherwise you will display your ignorance of tie clip etiquette.
The tie clip should be closer to your neck than to your stomach. This doesn't mean it should be right against the knot, but it should be a little more than halfway up the tie.
Tie clips can be worn either straight across or at an angle. Wearing a tie clip at an angle is more rakish way to wear it, so you should think carefully before you do this. If you're going on a date, wearing it at an angle is probably fine. If you're going to an important meeting with a client, though, it should be straight across. Even if you are on a date, its angle should not be more than 45 degrees.