The dividend yield is the rate implied by the sum of the amount of last 4 dividend payments per share divided by the share price.
BBY's price is 26.20 and shows a yield of 2.6% based on the last 4 dividend payments of $0.17 per share. So your logic is right, the yield times the value per share would approximate your dividend payment per share.
If you use the current Market Cap, it would give you the total approximate dividend payment for that time period.
Check out www.investlikeme.blogspot.com. There is an article on getting started in the market and how to read a stock profile. The author also shares his own personal portfolio which you can follow along with on twitter.
I have 500 shares of BBY, the next dividend date is 3/18/14, and the dividend yield is 2.6%. If the value of the shares is (let's say) $12000, on the dividend date, would the amount of dividends be .026 x 12000?