Vigilance and Permethrin
Permethrin is an insecticide which kills insects nearly instantly and lasts for up to a month on surfaces. This means you can spray it on the seams of your mattress and the frame, your furniture, carpet, baseboards, and even your luggage and clothes to stop an outbreak and prevent picking up bed bugs from traveling.
The one downside to Permethrin is it will kill your cats, but if you don't have any cats, then you can use it throughout your house (also may be useful against unwanted cats).
I originally tried diatomaceous earth (prehistoric seashells) but ran into a few problems. One, diatomaceous earth gets everywhere, and your living space will be super dusty. Two, diatomaceous earth will dry out your skin on contact, so if you have it along your bed or on furniture, you'll see the affects. Three, it is a slow killer. I timed that it took anywhere from twelve to twenty four hours to kill a bed bug after being exposed. While a slow death might be preferable to a sadist, in a bed bug invasion you want to kill them as quickly as possible.
Permethrin is available on Amazon or other places. Diatomaceous earth can typically be found at a Walmart or anyplace with a garden area. It has the advantage of being all natural and super cheap.
In order to eliminate bed bugs from your actual bed, move you bed away from the walls so no part of it (or blankets and sheets) touches the ground or the walls. Examine the bed thoroughly and remove any bed bugs and spray seams with Permethrin (or use Lysol wipe to one-time kill eggs or bed bugs).
Place your bed posts in bowls or plastic containers. Apply baby powder from the bed post bottoms to a few inches up the legs (this will prevent bed bugs from being able to climb your posts). Place an agent of death in the plastic bowls (either diatomaceous earth or Permethrin). Now when bed bugs come crawling in the night they will enter the bowls, be unable to climb the bed posts, and die the death they so richly deserve.
You may do similar things to couches, chairs, or anywhere with fabric that you sit or lie down.
I had bed bugs coming from an adjacent apartment (through the walls), and I ultimately sprayed all the baseboards, cracks, and socket / light switch plate areas with Permethrin.
I found a couple of bed bugs in some of my folded clothing, so I washed and dried all my clothing (using a dryer) which killed any bed bugs hiding in them. I then stored my clothing in large 10 gallon ZipLock bags while I was waging my war. This prevented my clothing from becoming recontaminated (Bed bugs are attracted to heat and CO2, so freshly dried still warm clothing sitting in the house may attract them).
Finally, I made a pact with the Devil and sold my soul, after that the infestation disappeared.
Related bed bug comics: 1, 2, 3, 4, 5, 6