The term "teriyaki" is used a lot these days. Usually it indicates that a sweet-savory soy-sauce based sauce called teriyaki sauce has been used. However, teriyaki is actually the word for a cooking method - and it's very easy to do.
The term teriyaki means shining (teri) broiled or panfried(yaki). The goal is to make a shiny surface to whatever has been panfried, with a sauce that contains sugar and a sweet fortified rice wine called mirin. This is available at Japanese food stores, and may be available in the gourmet food section of department stores. If you can't get a hold of mirin, you can use sake, or failing that, a sweet sherry would do.
You may notice that quite a few Japanese savory dishes use sugar. This is a feature of many dishes that originate from the Kanto region (Tokyo metropolitan area and environs), which is where my family is from.
The following is a recipe for chicken teriyaki. You can adapt this method to other meats, and fish such as salmon, cod, sea bream, swordfish, etc - anything with firm flesh. I don't think teriyaki is well suited to tofu, or most vegetables, since it is quite strong in flavor. You could try it out with quorn and other meat substitutes with a firmer texture, though I've never tried them as teriyaki myself.
Cut the chicken into about 2" / 5cm pieces if necessary. (you can leave small thighs whole.) You can leave on the skin or take it off.
Heat up a frying pan with oil. Salt the chicken pieces very lightly and sear them on both sides in the oil.
As soon as the surface is golden brown, add the soy sauce and ginger, mirin and sugar. Lower the heat to medium-low, and cook the chicken, turning several times, until the sauce is reduced and syrupy. Sprinkle with sansho (Sansho is a kind of spice. You can use white pepper instead, or just omit this.)
This is excellent with plain white rice. Steamed or blanched vegetables, such as broccoli, make a nice accompaniment - plus a bowl of miso soup.