There are around 70 species of cockroaches in North America. Most measure between ⅝ and 1¾ inches. They come in varying shades of brown and black, have six spikey legs, long (sometimes body length) antennae, and most have wings with which they may or may not be able to fly, depending on the species.
German Cockroach
American Cockroach
Oriental Cockroach
Smokey Brown Cockroach

In their wake, roaches leave slimy feces, secretions, regurgitations, shed exoskeletons, and egg cases, not to mention that charming cockroach stink. Besides being gross, cockroaches are a health risk (asthma, allergies, infection, food poisoning, hepatitis, and other maladies). This is why people panic and reach for chemicals first. The panic strategy may kill cockroaches, but some will survive and become resistant to your chemicals. And without making other changes to your behavior and property, you leave yourself open to a future cockroach infestation.
Use cockroach traps to determine where roaches are hiding. Roaches hide together. To locate their harborages, buy lots of cockroach traps and place them all over your home. Concentrate on areas where they've been seen and areas with a foul odor, brownish or rust-colored streaks, exoskeletons, and body parts. Also place traps along walls, in corners, near plumbing, near appliances, and in drawers, cabinets, cupboards, and closets. I recommend plain, unscented sticky traps for mice and insects. You can also use more expensive roach traps that lure roaches in with roach baits and pheromones. Monitor traps for a full week. Full traps—especially traps filled with nymphs (immature cockroaches)—indicate that a cockroach harborage is nearby.
Deprive cockroaches of food. Start a strict regimen of sweeping, vacuuming, cleaning, and dish doing. Next, go through the kitchen and put all the food in roach-proof containers. Since they'll eat just about anything, contain and/or dispose of as much clutter as possible. Many species of roach will move from the yard to the home, so organic waste must be properly disposed of both inside and out. Inside, use an airtight, five-gallon bucket (found at paint and hardware stores) lined with a thin plastic bag for all food scraps. Outside, make sure the trash can is sealed tight and switch to a contained composting system. Finally, don't leave pet food and water dishes out.
To control cockroaches, you'll need to deprive them of water. Most cockroach species are very vulnerable to dehydration without a constant water source. Insulate cold water pipes to prevent condensation. Pipe condensation is a common source of water for cockroaches. Look for leaky pipes . . . and fix them. Install screens over all drains or use drain caps. This will prevent entry through drains, but it will also prevent cockroaches from enjoying the moisture left on drain traps. Be aware that potted plants and flowers in vases are often watering holes for cockroaches. Lastly, increase ventilation to damp or moist areas. This can be especially beneficial in attics and basements. Many cockroach-infested homes benefit from the use of a dehumidifier.
Indoors, seal all cockroach harborages. Cockroaches can fit into surprisingly small spaces. The most common pest species, the German cockroach, can hide in spaces as small as 1.5 millimeters. Seal off all cracks, nooks, and spaces around trim and baseboards, pipes (where they meet walls), shelves, cupboards, cabinets, sinks, and bathtubs using caulk and/or paint. Focus on areas where your sticky traps captured the most roaches. Before you seal off the cockroach harborages, clean the areas with a vacuum, soap, and water (this will make roach control chemicals more effective) and treat the cracks and crevices with any roach-killing product that can be worked into tight spaces. This will prevent cockroaches from living to seek out new harborages.
Deny indoor access to outdoor cockroaches. Walk around your house's perimeter with a caulking gun and fill in every crack, crevice, and hole you spot. Look around wires and pipes entering the home, around outlets, lights, and vents, areas where siding meets foundation, and at corners. Apply bug screens to all vents, weather stripping to all doors and windows, door sweeps to doors, and patches to holes in window screens. Finally, keep a clean, dry border around your home. Pick up leaf litter, remove thick vegetation and/or mulch, move wood piles back, and keep plants trimmed well back from the siding and roof. If the outside of your home is less habitable, it's less likely cockroaches will find their way in.
Kill cockroaches with baits, dusts, sprays, and/or foggers. Because roaches frequently develop poison resistance, it's good to purchase several different types/brands of cockroach poison. In general, it doesn't matter what brand you get. (If, however, you want recommendations, please contact me.) What matters is that they're used in accordance to the directions. Baits are available as stations or gels. Bait stations are those little black hockey pucks that roaches crawl into and eat from. Gels are gels. Along with your baits, use dusts or roach sprays for application into hard-to-reach places. For severe infestations, consider using a fogger. They're effective and achieve swift results. If your problem is primarily outdoors, there are spreadable granule products available.
Continue placing sticky traps to monitor for progress and reinfestation. I would recommend leaving sticky traps out at all times. This way, if cockroaches return or you didn't get rid of them as thoroughly as you thought, you'll quickly find out. If you're worried about kids or pets messing with your sticky traps, products like Protecta Pets Monitors come with a hard plastic protective housing.
Cockroach control is mostly the same no matter what species you're dealing with, so don't go crazy here. By the numbers, you're probably dealing with the German cockroach, which is by far the most common pest. But if not, knowing the species can be of value. If you're dealing with an Oriental cockroach, place more traps (and possible treatments) in basements and crawl spaces, as they like the cooler temperatures and moisture. Knowing that you have a Smoky Brown or Brown cockroach will compel you to do some landscaping outside. Also, some roach control products specifically target some species but are useless against others—so read those labels. The common pest cockroach species are featured in the left sidebar.

Control cockroaches with diatomaceous earth. DE is a natural insecticidal dust made from the fossilized remains of ancient algae called diatoms. It's food grade—it won't harm you, your family, or your pets. It feels like talcum powder to us, but when cockroaches walk over it, they develop cuts in their exoskeleton, dehydrate, and die. DE should be applied in very thin layers (if too thick, the cockroaches will walk around it) using a hand duster into cracks and crevices and roach "runways" and hotspots. Barrier treatments can also be applied around homes.

Use boric acid for killing roaches. Boric acid (Borax), like DE, is a desiccant dust. However, it also works as a stomach poison. The cockroaches absorb the stuff through cuts and by ingestion. Unlike many chemical products, cockroaches have not developed any resistance to boric acid, nor are they repelled by it. They stupidly walk all over it while you laugh deeply, and from the belly. Boric acid is applied (thin layer only) using a bulb duster, but care should be taken to only use it in cracks, crevices, and out-of-the-way places it won't be ingested by children, pets, or yourself.

Make some cheap, homemade traps. For both population monitoring and reduction, you can make simple, effective cockroach traps with glass jars or coffee cans. For bait, place a chuck of bread soaked in beer in the jar. Roaches go crazy for beer. (Great excuse to get drunk: "I'm killing roaches, honey.") Next, spread petroleum jelly over the upper, inside of the jar to prevent the roaches from escaping. Depending on the species, you may need to experiment with baits. They generally go for carbohydrates or sweet things like syrup.