The Reuben Sandwich, although the true origins are a mystery, Was created in the United States somewhere between 1915 and 1930. There are several variations to the sandwich and depending on my mood, I will vary the ingredients.

Supplies

The main ingredients to the Reuben sandwich are:

Rye Bread - A good rye bread is important. My favorite is a marble Rye, but I will use a seeded Rye, or a solid Rye bread. It depends on what is available when I go shopping for bread.
Pastrami. - The Pastrami should not be real thick. I prefer thin enough that it could be shredded with with my hands if I want to. I have also used Corned Beef, but Pastrami is my favorite.
Sauerkraut - The fresher the better. I make my own Sauerkraut, so I know the quality. Most people think of Sauerkraut as being being white, made from a green cabbage, but if you make it yourself, you can also make your sauerkraut from a red cabbage to give it a different flavor.
Dressing - Dressing is typically either Russian Salad Dressing or Thousand Island dressing. Russian is more tangy, while Thousand Island is more smooth. I choose this a lot of times depending on what I am having with my sandwich.
Swiss Cheese - a good quality Swiss cheese is used to finish the sandwich. .

Step 1: Saute the Sauerkraut.

To get the sauerkraut ready for the sandwich, put it in a pan and saute it. When cooked, it will be softer and will reduce in size about half. I will usually use about 1/2 to 3/4 a cup. Time to reduce it is only about 5-10 minutes.

With this sandwich, I used both sauerkraut from both a green and red cabbage.

Because I saute up my sauerkraut, sometimes for a different flavor, I can saute some onions and peppers with it.

Step 2: Heat Up the Pastrami

After a couple of minutes of sauteing the sauerkraut, I will add the pastrami to the pan and heat it up as well. This helps the sandwich to be thoroughly heated through. The pastrami does not need to cooked, just heated up.

Step 3: Adding Cheese

Adding the cheese can be done two ways, depending on how firm you want the cheese.

Place the cheese directly on the bread like you would make a toasted cheese sandwich.
Place the cheese on the sauerkraut or pastrami while it is being sauteed like you would a Philly steak sandwich.

Step 4: Assembling and Cooking the Sandwich

Put the sandwich all together.

The argument on the order of placement of meat and condiments is personal preference, but this is how I assemble it:

On a heated skillet or frying pan, spread butter on the cooking area

Add slice of bread
Add Cheese (if not cooked with the sauerkraut)
Add meat
Add dressing
Add Sauerkraut
Add top slice of bread.

Heat the sandwich on the grill until it is toasted on the one side. Carefully flip the sandwich over to cook the other side. When done plate it and cut it.