If there was any doubt that volatility now rules the market, today we got an answer.

If you didn't watch the market all day today, you could have missed the schizophrenic mood the market is in. A day after the Dow Jones Industrial Average fell more than 600 points, the index swung 640 points from low to high in just over an hour to close the day, ending 4% above yesterday's close. Over at the Nasdaq, stocks rocketed more than 5% higher to end the day.

As Vince Lombardi would say, "What the hell's going on out here?"

It all started with the Fed
Most of the volatility happened in a two-hour period, as the market tried to figure out exactly how to digest the Federal Reserve's latest policy statement. At first there was a feeling of "here we go again," as the Dow fell nearly 500 points just after 2 p.m. ET.

Maybe investors were disappointed that the Fed didn't announce any stimulus plans, but whatever got sellers excited, the drop was short-lived and buyers rushed the market. Stocks went up, oil ran higher, and even Treasuries screamed higher after the Fed gave a sure answer on where short-term rates were headed.

For the first time in recent memory, the Fed added a definitive time frame for low rates, saying they would remain where they are through "at least" mid-2013. With rates guaranteed to be low for two years, the two-year yield reached a record low of 0.17%. That's almost like keeping money in a tin can buried in the yard.

With diversified companies such as 3M (NYSE: MMM) and General Electric (NYSE: GE) sporting long-running dividends and paying investors more than Treasuries offer, we could see a move to these relatively safe stocks. I can't imagine that people will continue to flock to Treasuries with yields this low -- although crazier things have happened.

Banks are loving this
Some of the biggest beneficiaries today were banks, which traded dramatically higher by the end of the day. Bank of America (NYSE: BAC) led the way, climbing 17%, while Citigroup (NYSE: C) and Wells Fargo (NYSE: WFC) jumped 14% and 8%, respectively.

Low rates from the Fed means low borrowing costs for banks and should mean greater profits for investors.

If mortgage rates fall, as some are predicting, maybe we could even start to see a recovery in housing. Or maybe that's just wishful thinking.

Oil can't decide which way is up
On the downside (for a while), oil slid as much as 7% in the past 24 hours as investors worried about slow economic growth. After last week's anemic GDP numbers, the Fed said it expected slower growth, which should mean less demand for oil. That sent ExxonMobil (NYSE: XOM) into the No. 2 spot on the market-cap list behind Apple (Nasdaq: AAPL) for some of the day.

But oil and oil stocks rebounded like the rest of the market later in the day, as investors bought almost anything they could get their hands on.

Tune out the noise
What can we learn from a day like today? Turn down CNBC, be on the lookout for opportunities, and don't be afraid to act when the market is panicking the most. You might be rewarded on a day like today.

Since we can't predict the market's mood swings, Foolish investors would be wise to buy when a value presents itself and turn off the real-time ticker. This Fool was so focused looking for great values that I didn't have time to worry about what my stocks were doing on a minute-by-minute basis during the day. That may be the only way to stay sane in a market like this.

What was your reaction to today's market? Were you a buyer or a seller? Leave your thoughts in our comments section below.