How To make a Smoke Bomb

The smoke bomb you would purchase from a fireworks store usually is made from potassium chlorate (KClO3 - oxidizer), sugar (sucrose or dextrin - fuel), sodium bicarbonate (otherwise known as baking soda - to moderate the rate of the reaction and keep it from getting too hot), and a powdered organic dye (for colored smoke). When a commercial smoke bomb is burned, the reaction makes white smoke and the heat evaporates the organic dye. Commercial smoke bombs have small holes through which the smoke and dye are ejected, to create a jet of finely dispersed particles. Crafting this type of smoke bomb is beyond most of us, but you can make an effective smoke bomb quite easily. There are even colorants you can add if you want to make colored smoke. Let's start out with instructions for the easiest/safest type of smoke bomb you can make: 

Smoke Bomb Materials

sugar (sucrose or table sugar) 
potassium nitrate, KNO3, also known as saltpeter (buy it online or you can find this at some garden supply stores in the fertilizer section, some pharmacies carry it too) 
skillet or pan 
aluminum foil 

Once you've gathered your smoke bomb materials, it's easy to make the smoke bomb...
Pour about 3 parts potassium nitrate to 2 parts sugar into the skillet (5:3 ratio is also good). Measurements don't need to be exact, but you want more KNO3 than sugar. For example, you can use 1-1/2 cups KNO3 and 1 cup sugar. If you use equal amounts of KNO3 and sugar, your smoke bomb will be harder to light and will burn more slowly. As you approach the 5:3 KNO3:sugar ratio, you get a smoke bomb that burns more quickly. 
Apply low heat to the pan. Stir the mixture with a spoon using long strokes. If you see the grains of sugar starting to melt along the edges where you are stirring, remove the pan from the heat and reduce the temperature before continuing. 
Basically you are carmelizing sugar. The mixture will melt and become a caramel or chocolate color. Continue heating/stirring until the ingredients are liquefied. Remove from heat. 
Pour the liquid onto a piece of foil. You can pour a smaller amount onto a separate piece, to test the batch. You can pour the smoke bomb into any shape, onto an object, or into a mold. The shape and size will affect the burning pattern. 
If you aren't going to clean your skillet immediately, pour hot water into the pan to dissolve the sugar (or else it will be harder to clean). Clean up any residue you may have spilled out of the pan, unless you want mini-smoke bombs on your stovetop. 
Allow the smoke bomb to cool, then you can peel it off the foil.
The solid smoke bomb material is flammable and can be lit directly. You can light your smoke bomb using a lighter, preferably one of the long-handled types used for barbeque grills. Only light your smoke bomb in a well-ventilated area, on a surface that won't catch fire. The smoke bomb will burn vigorously (more slowly with a higher percentage of sugar) with a purple flame. 

Alternatively, you could place a short length of wick into the smoke bomb when you pour it, and then light the wick. 

There are additional recipes for smoke bombs...
No-Cook Smoke Bomb or Powdered Smoke Bomb 

A variation on the saltpeter/sugar recipe is to replace the granulated sugar with powdered sugar (icing sugar). The powdered sugar and potassium nitrate are sifted or mixed together and left in powdered form. The powder is ignited to form smoke. 

Zinc & Sulfur Smoke Bomb 

Zinc Filings - Zinc Powder 
Sulfur Powder 
Mix the zinc and sulfur. Insert a red-hot wire to ignite the mixture and produce smoke. This is a particularly smelly smoke bomb. 

Black Powder Smoke Bombs 

Black powder (gunpowder) or pyrodex can be mixed with other substances to produce a lot of smoke: 
as a powder, mixed with sugar and sulfur 
mixed with sawdust 
with sugar, sulfur, and a bit of material from a road flare (red flame) 

It's easy to make a colored smoke bomb... 

Recent Chemistry Features
The recipes for colored smoke bombs require chemicals that may not be readily available unless you have access to a chemistry lab, but it's worth knowing how it's done. Parts or percents are by weight. The ingredients are sifted together and ignited to produce the smoke. 

White Smoke Recipe 

Potassium nitrate - 4 parts 
Charcoal - 5 parts 
Sulfur - 10 parts 
Wood dust - 3 parts 

Red Smoke Recipe 

Potassium chlorate - 15% 
para-nitroaniline red - 65% 
Lactose - 20% 

Green Smoke Recipe 

Synthetic indigo - 26% 
Auramine (yellow) - 15% 
Potassium chlorate - 35% 
Lactose - 26% 

Reference: The formulations for colored smoke bombs came from Wouter's Practical Pyrotechnics, who cited the recipes as originating from L.P. Edel, "Mengen en Roeren", 2nd edition (1936). 

You can also make a smoke bomb with colored flames...
It's fairly easy to make colored flames by adding these chemicals to your smoke bomb recipe: 

Chemicals Used to Color Flames 

Red - strontium salts, most easily found in road flares 
Orange - calcium chloride (laundry bleaching agent) 
Yellow - sodium nitrate (common in chemistry lab) 
Green - barium salts, such as barium nitrate (common in chemistry lab) 
Greenish-Blue - copper sulfate (common in a chemistry lab, also found in many algicides for pool treatment) Blue - copper chloride (common in chemistry lab) 
Purple - potassium permanganate (common in a chemistry lab, also used in sewage or water treatment) 
White - magnesium sulfate (epsom salts, found on laundry aisle or in a pharmacy) 

Essentially, you are adding metal salts to get colored flames. You may get additional ideas from looking at the Flame Tests, Fireworks Colors, and How to Color Fire tables. The metal salts listed here produce a relatively safe smoke. Use caution when considering other metals salts, as some compounds may produce toxic smoke.