Serving as a volunteer in a larger city in the southwest US, I will share briefly some things I learned about a bed-bug infestation we had at our apartment (by no fault of my own, mind you).
A lot of the homes we went into were teeming with little crawling surprises, and many of our appointments were at old homes with trashy yards. Anyway, I don't know exactly where they came from, but it's not too hard to figure it out... I got transferred into the area and apartment just after the infestation was discovered and measures were taken against it.
hippitrail's answer was thorough and accurate from my experience. All our our mattresses and box springs were on the concrete in front of the apartment, sunbathing, eventually thrown away. The bed bugs don't like the heat.
Before we got new beds we slept on counters, table chairs, anything that wasn't cushioned and was off the ground... we had a pest control guy come in and spray some crazy chemical all over; this seemed most effective.
Interestingly... when we did get new beds, we were careful to check them daily especially in the creases of the mattresses and tight areas of the box springs. Bed bugs like tight places that squeeze a little, it seems. Even on our new beds we were getting bitten. The bites stopped the day I moved my bed away from the wall. Apparently, they were coming out from under the carpet (I think?) and crawling up the wall, into the bed, and biting.
We kept our eyes open always and had over-the-shelf chemicals at the ready when we saw them crawling on furniture, us, or the walls. We tore apart the cushions on the chairs and couches, sprayed them with household chemicals, and let them sunbathe for a while before putting them back.
Each evening when we came into the apartment, we undressed and washed the clothes right away. We kept all clothing off the floor and away from walls. Still, somehow I'd find little critters crawling around on my clothing. All we could do any more was kill each one we saw.
By the time I left the area 4 months later, the bugs were gone: not a sight of a single one.