Google AdWords allows you to pay to advertise on Google based on keywords. You'll show up in the top 3 or on the right column based on your bid for keywords relevant to your business. It can be expensive but there are ways you can keep costs down and control your budget to get the most for your advertising dollars.
Google doesn't care how compelling your site is but you do because it's what drives your potential customers to contact you for more information. If a potential customer calls you, you're likely to convert that call into a new customer. This is why you need a compelling 'landing page'. It can be the home page or another page with a contact form, specials or sale information, newsletter sign up, etc.