Nice, unbiased post Michael - good to see
Terry - this is a VERY brief, simplified explanation,
If you do a Google search for a service, more often than not you'll see 'Ads related to...' on the top of the page, above the 'organic' listings, as well as down the right hand side, and on the very botto of the page. These are Adwords ads created by/for the advertiser - you can specify what you want the ad to say, and what website/page you want the ad to link to (as long as it complies with Google's T&Cs).
First you choose which area you want to cover - for most carpet cleaners a radius of 5-10 miles is sufficient. Then, you compile a list of keywords for which you want your ad to show - 'carpet cleaners, upholstery cleaners' etc etc. Then you set a 'max bid amount' - that is how much you are willing to bid to have your ad displayed when those terms are searched for.
Next, you create some ads to show when your keywords are triggered, and decide what page you want to redirect to (carpet cleaning search to carpet cleaning page, upholstery cleaning page to upholstery, for example).
Once that is completed, your campaign can go live. Every time someone searches for the keywords you have chosen, Google runs an extremely fast 'auction' for everyone in the relevant area who has elected to use those keywords for their campaign. The auction takes into account several factors, most importantly:
Max click bid
'Quality' Score
Your quality score is how relevant the search is to your advert & your website - Google don't want people who are searching for rug shops to find carpet cleaners (if that makes sense??). The higher your bid and better your quality score - the higher up the page your ad will appear (and therefore, more likely to be clicked on).
If your ad gets displayed 100 times, but never clicked on (maybe your ad is poor or not ranking high enough due to the above factors) then it will cost you no money at all. Adwords is a PPC (Pay-per-click) service - which means you only pay when users actually click on your ad. Of course, if they get to your website and don't like what they see - then you've paid for nothing, that's why Adwords definately works, but is only a small cog in the machine.
I hope you can make some sense out of that post, and I've not left you more confused than before I started
I'm going for a lie down!