If you don’t happen to have a dedicated panini press, and you don’t want to go out and buy one, you can get pretty much the same effect with 2 frying pans of unequal size and a big can of tomatoes (or a brick, or other heavy object). Just place the prepared sandwich(es) in the larger pan over the flame, balance the smaller pan on top of the sandwiches, and put the heavy object in the smaller pan. This will apply just the right amount of pressure to squash the panini while they cook to a perfect doneness.

As to ingredients, the sky's the limit - but I do have a few rules of thumb.

1) Use substantial bread that will not squash down too much or fall apart. Something with a good crust is best. Match the flavor to the filling.

2) Apply some kind of tasty spread to the inner sides of both bread slices. This can be flavored mayo, aioli, chutney, prepared salad dressing, or any kind of weirdo condiment - but I would not use butter or oil, since you will use that on the outside to cook the sandwich, as you do with grilled cheese.  

3) Use some cheese, which will melt and glue the whole thing together. It can be grated or thinly sliced.

The filling can come out of the dark corners of your fridge, and this can be a great way to use leftovers. Any kind of precooked meat, pickles, tomatoes, capers, omelets, fruit, peppers, fresh herbs - use your imagination.

Some Recipe Links

Italian Panini - This page from "Cuisine at Home" magazine offers general advice on panini cookery (much more profound than what I have given above), and a tasty sounding recipe.

Pressed for Success - Three recipes by Adam Ried. I have tried the Sausage Panini with Pepper, Arugula and Asiago, omitting the arugula and substituting Swiss cheese, and this was very good.

Grilled Eggplant Panini - From the NY Times. Haven't tried it.

Prosciutto and Fig Panini - From Epicurious. This one is a good candidate for substitutions, to cut down on price (and bother).