Depends on where you are, but most regions in most countries have at least one profesional manufacturer that takes care of the pick and place part.
The place where I have my stuff made (
http://www.amset.sk/ ), will take even single board orders. There is a one time setup fee obviously (depending on project complexity it can be anywhere from 100 EUR to hundreds of EUR (really complex, big boards)), after that you pay per 1000 shots (a few EUR).
I'd say the first step is to locate someone in your area.
Step 2 is contacting them and asking what they need and how much will it cost.
The place where I get my stuff made can work with pretty much any type of operation - from "you send the gerbers and BOMs, we ship you a fully assembled PCB, truholes included and even take care of the buying of exotic parts" to "bring us the boards, parts and everything, we'll just put them through our machine".
It's not that hard or expensive these days - you can get single piece quantities with no obscene initial costs.