I took my first investing class as a teenager, and one moment stands out in my memory. A fellow student asked the instructor, a stockbroker, about dividends.

"Dividends?" he asked. "I'm trying to make my clients wealthy. You don't do that waiting for tiny checks in the mailbox every quarter."

Even then, I had enough horse sense to know he was wrong. Paying attention to dividends is exactly how you become wealthy over time.

Wharton professor Jeremy Siegel made a wonderful discovery in his book The Future for Investors. The greatest long-term returns typically don't come from the most innovative companies, or even companies with the highest earnings growth. They come from companies that happen to crank out dividends year after year. Simply put, since the 1950s, "the portfolios with higher dividend yields offered investors higher returns."

Market commentary regularly centers around price gyrations, yet dividends have historically accounted for more than half of total returns.

Reinvest those dividends, and it's even greater. Take Reynolds American (NYSE: RAI) for example. Since the late 1990s, Reynolds' share price has increased 300%. But add in reinvested dividends, and total returns jump to 840%:

Source: Capital IQ, a division of Standard & Poor's.

There's no ambiguity here: Over time, Reynolds' share appreciation alone has paled in importance to the power of its reinvested dividends. The results are similar for competitors Altria (NYSE: MO) and Lorillard (NYSE: LO); reinvested dividends skew both companies' total long-term returns dramatically higher. If you're a long-term shareholder, don't worry about daily share wobbles. Devote your attention those dividend payouts and your commitment to reinvest them.

And how do Reynolds' dividends look? At 6.3%, its yield is one of the highest you can find among large stocks. That dividend payout has grown by an average of about 7% per year for the past decade. Dividends have used up the majority of free cash flow in recent years, but this has become fairly standard in the tobacco world, where declining smoking rates in the U.S. have limited opportunities for expansion. And while smoking rates have indeed been falling, tobacco companies' ability to raise prices has offset any material decline in revenue. Reynolds should generate significant cash flow in future years, maintaining its reputation as a quality dividend stock for the foreseeable future.

To earn the greatest returns, get your priorities straight. What the market does is less important than what your company earns. What your company earns is less important than how much it pays out in dividends. And what it pays out in dividends is less important than whether you reinvest those dividends.