What is the best way to advertise our home remodeling business and how much would it cost?

There are many ways to advertise your business in today's market. Newspaper, I suggest that you only advertise in newspapers that have a circulation of 100,000 or more. You can advertise on the internet. You can open up your own webpage, for fairly cheap, and help pay for it by placing Google ads on your page, and a Google toolbar on your web page. You could also hang up fliers with tear-off tabs that contain your contact information, at public places like grocery stores and laundromats. There is also word of mouth, or you could be a walking ad and make clothes that advertise your business.
Word of mouth is the best way to grow your type of business. The next thing is to advertise in your local area newspapers - size doesn't matter. A small town paper is just as effective as a large town. We had a painting/wallpapering business 15 years ago and advertised in the papers and did ok. When our yellow pages ads came out we pulled our newspaper ads and almost went under. The yellow pages did nothing for us. We lived in the Chicago suburbs so lots of business potential. Make sure your vehicles have your name on them so when you are parked in front of a customer's house, the neighbors can see who you are and take down your name and number. Network through local suppliers you use - i.e. home centers, paint stores, hardware stores. Many times customers will ask their local stores if they can recommend someone. Good luck!