To make it, you take two pieces of bread, and place a slice of cheese and a slice of meat in the middle.
The cheese used is often American-style Swiss cheese.
The meat is usually cold-sliced chicken, turkey or ham, or a combination thereof, with chicken or turkey being more prevalent overall since the 1970s.
Dismiss the claims of purists who say the meat can only be ham; poultry has in fact been called for in recipes since at least the 1950s.
The top and bottom of the sandwich are dipped in beaten egg, sometimes beaten egg with milk, then the sandwich is pan-fried in butter.
Traditionally, a Monte Cristo Sandwich is served with a small pot of jam on the side.
A variant calls for dipping the sandwich in a batter, and deep-frying it.
In February 2008, Esquire Magazine rated the Monte Cristo at Canter’s Deli in Los Angeles as one of the best sandwiches in America.  Theirs is “Turkey, Ham & Swiss, Dipped in Egg & Grilled on Egg Bread Served with Powdered Sugar & Jam.” Restaurant photos also show it coming with a small fruit nappy of fruit cocktail. The 2011 price was $14.75 US.
The “Trailer Park Monte Cristo” made at the Beachland Ballroom in Cleveland, Ohio consists of a peanut butter and jam sandwich, dipped in pancake batter, deep fried, and served dusted with icing sugar (aka powdered sugar.) 
Monte Cristo sandwiches are of American origin.
Some sources credit the sandwich’s invention to the Monte Cristo Hotel in Everett, Washington, in its second building erected in 1925 . The hotel itself was named after the Monte Cristo mining region in the Cascades Mountains. The sandwich, though, actually seems to predate that incarnation of the hotel. We have found references to the sandwich as early as 1923.
This is the earliest known recipe to date, from 1924:
“Cover six slices of sandwich bread with a slice of American full cream cheese [Ed: sic], cover the cheese with slices of boiled ham, cover with slices of bread, tie with white string, dip in beaten egg and fry a nice brown on both sides in hot butter. Place on hot plates, remove the string and serve.” — Wyman, A.L. Practical Recipes: Help for Epicures and All Who Appreciate Good Cooking. Los Angeles, California: Los Angeles Times. 24 May 1924. Page 6.
Some sources speculate that Monte Cristo sandwiches were based on Croque Monsieur sandwiches. However, the earliest primary source CooksInfo.com has for Croque Monsieur in American print dates from 1943 (see separate entry on Croque Monsieur), 20 years *after* the first reference to Monte Cristo sandwiches in 1923, which would put that speculative origin decidedly out of the running.
Other sources speculate that Monte Cristo sandwiches were based on something called a French sandwich, recipes for which emerged in the early 1930s:
French Sandwich: Six slices bread; 1 can tuna; jar mayonnaise; jar pickle relish; sliced tomatoes; lettuce; 2 eggs, beaten. Dip bread in beaten eggs, and fry in fat on medium heat. Place on plate, put lettuce leaf on bread, chilled tuna mixed with mayonnaise and pickle, and add slice of tomato. Serve hot.” — Schwin, Mary. Cooking School Recipes. Ogden, Utah: The Ogden Standard. 28 April 1933. Page 15.
One could also speculate a link to the Reuben sandwich, which emerged around the same point of time.
There is perhaps a bit of reason to speculate that the Monte Cristo sandwiches has a west-coast America origin, given the preponderance of early references to it in western states (as seen in the citations below.)
“Chef “Joe” Beyl will present three of his most popular recipes for the late-supper menus: “Lobster Thermidore,” “Monte Cristo Sandwich” and “Tomato Stuffed with Tuna.” Detailed recipes for these will be furnished to all persons attending.” — Martha Lee Home Economics Department advertisement in : Oakland Tribune. Oakland, California. 20 September 1936. Page 4s, col 7.
“Mrs. Elliott Scott postcarding back from Hollywood that you haven’t lived until you’ve eaten one of the Monte Cristo sandwiches at the Brown Derby.” — Davis, Jeff. “Around the Plaza” column. San Antonio Light. San Antonio, Texas. 28 July 1937. Page 1, col. 1.
“Monte Cristo Sandwich 75c.” — Advertisement for Club Fortune, Reno Nevada. Appearing in Nevada State Journal. 17 September 1942. Page 1.
“MONTE CRISTO SANDWICH, French fries 90c.” — Advertisement for Moulin Rouge, Reno Nevada. Appearing in Reno Evening Gazette. 26 April 1949. Page 8
Recipes as early as the 1950s called for chicken:
Here a writer says the recipe is ideal for “leftover turkey, ham or chicken.” (Note that he calls for a 2 layered-sandwich.)
Butter a slice of white bread and cover with slices of baked ham and turkey (or chicken), white meat preferred. Butter a second slice of bread on both sides and place atop meat. Cover with 2 thin slices of swiss cheese.
BUTTER A THIRD slice of bread on one side and place buttered side down on the cheese. Trim away the crusts and cut the sandwich diagonally in two. Secure the halves with toothpicks and dip in beaten egg. Saute them gently in melted butter on both sides until golden brown. Remove the picks and serve with cranberry sauce or red currant jelly. This is a treat for luncheon or a light supper.” — Fynn, Charles E. Mostly for Men column. Chicago, Illinois: Daily Herald. 8 January 1970. Section 2, Page 1.
In 1966 the Tahitian Terrace and Blue Bayou restaurants in Disneyland, California, put Monte Cristo sandwiches on their menus, which perhaps helped popularize the sandwich. The Disneyland version was, and is, deep-fried. 
Literature & Lore
Here’s one of our newly discovered favorites which we first tasted in Disneyland. I have a new cookbook, “Disneyland Fun Food Cook Book” and it includes this favorite sandwich.
BLUE BAYOU MONTE CRISTO SANDWICH
1 ounce slice white meat of turkey
1 ounce slice ham
1 ounce slice Swiss cheese
2 slices white bread
Make a sandwich with turkey meat, Swiss cheese and slice of ham. Be sure to place the Swiss cheese between the turkey and ham. Cut sandwich in quarters. Use toothpicks to hold sandwich together. Dip sandwich in egg batter and fry in 360 degree oil until golden brown. Remove toothpicks, sprinkle with powdered sugar. Serve with blackberry jelly and a fruit compote topped with coconut.
1 1/2 c. all-purpose flour, sifted
1/4 t. salt
1 T. baking powder
1 1/3 c. water
Sift flour, salt and baking powder together. Add water to beaten egg and add to flour mixture, mixing well. Yield: 2 cups batter.
— Winters, Charlene. Kitchen Classics column. Provo, Utah: The Herald. 9 January 1977. Page 38, Col 1.
 Belloni, Matt et al. The Best Sandwiches in America. New York: Esquire Magazine. 16 February 2008.
 O’Donnell, Larry. Building Up Everett: A Brief History by the Decade. Historic Everett Society. August 2007. Retrieved January 2011 from http://www.historiceverett.org/about.html
 Editors of Cook’s Country Magazine: The Cook’s Country Cookbook: Regional and Heirloom Favorites Tested and Reimagined for Today’s Home Cooks. Boston, Massachusetts: Boston Common Press. September 2008.
Pastorio, Bob. Foodlore Column: How Many Monte Cristos Can We Create? Harrisonburg, Virginia: Daily News Record. 21 June 2000. Page 15, Col. 3.