Does anyone have any experience with using Google AdWords?

[Joan of Fremont]

To regain your previous search rankings, make sure you use 301 redirects (permanent redirects) from the old URLs to the new URLs.

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Your ad shows up in the search results when you create an ad and bid on specific keywords. An ad cost from 15 cents per click and up (depending on your niche, it can be several dollars per click). But how high your ad shows up is not only determined by who pays the most.

Google Adwords ad placement is based both on how much you bid for the ad and factors that make up a "quality score". The more relevant Google thinks your ad is to the search, the better your placement/lower your cost for that placement. That means that a very good ad can show up first in the results above other ads that are actually paying more.

p.s. the "linkbacks" in the ads don't count as links in terms of your organic SEO value.

Your best bet to learn the basics of how AdWords works is to go to the Google AdWords help center.