The next few months could be the hardest of your investment life. But they may also be the most profitable.

The volatility will be rough. Citigroup (NYSE: C) is off its 52-week high by 60%. Google (Nasdaq: GOOG) is off 40%. So is AIG (NYSE: AIG). These aren't random companies. This is America's largest bank. The world's most profitable Internet company. America's biggest insurer.

These are supposed to be blue chips -- shares of the best, most dependable businesses in the country -- yet they're bouncing around like penny stocks. That makes investing tough.

Yet that volatility also provides opportunities. The market's giving you the chance to buy stocks for prices substantially lower than a year ago. The question is: Do you have the courage to buy the best opportunities when they are available?

Long-term investor? Really?
Many people claim to be long-term investors; they're confident they can ride out the periodic hiccups. But living it is something different. In a bear market, you don't just have to live through a few bad weeks. The turbulence can last for months or even years.

You'll be living in an environment where you get kicked in the teeth every day. You buy Headwaters (NYSE: HW) at $13 because it looks cheap, only to see it fall to $10 a few weeks later. Maybe it was cheap. But now it's cheaper.

It's tremendously difficult to act when everyone's claiming the sky is falling. People may believe that the most lucrative time to buy is at the peak of negativity, but only a small minority have the courage to actually go through with it.

Warren Buffett is one of those people: His huge purchase of American Express (NYSE: AXP) at the height of the Salad Oil Crisis is legendary. His ability to make excellent decisions during volatile times is one of the reasons he recently became the world's richest person.

It's hard to be as levelheaded as Buffett, but there are things you can do to make your attempt easier.

Blinders: not just for horses
First, tune out all of the noise. Turn off the financial TV shows -- they're just entertainment masquerading as investing wisdom. Ignore the hysterical headlines, and look carefully at the reasoning of any article.

Remember that even experts aren't great at predictions during a volatile market. According to the Atlanta Federal Reserve, economic predictions that were typically 60%-80% accurate in a stable market plummeted to a 10%-20% accuracy rate in more volatile times. Don't be quick to accept anyone else's conclusions.

Liquid courage
Second, make sure that your portfolio is filled with solid companies you believe in, no matter what the market does. Evaluate each stock you own, and decide how that business is likely to react to the environment. Hold on if you're confident about the company's long-term prospects, even if there might be some short-term negatives.

If there's a good chance that the business will take a permanent hit, think about selling. For instance, in March last year, I sold my position in Washington Mutual (NYSE: WM) because it seemed clear that the company would be under considerable stress during the housing bust.

By evaluating each stock on its own merits, you can be confident in the core value of your portfolio, even as some of those same stocks are falling. If you've chosen to selectively sell some of your investments, you will also have raised some cash right when you might really need it.

Get out the checkbook
Third, look for buying opportunities, because stocks are often sold indiscriminately during bear markets. Some companies will deserve the lower prices, but many won't.

Don't be reckless -- your reasoning should be based on solid fundamental analysis, not on where the stock used to be. Bear Stearns (NYSE: BSC) traded above $150 last year, and it may have seemed cheap at $75, but purchasers at that level have lost 85% of their money, with the stock now at $11. Make sure you focus on solid businesses that are truly undervalued, not just stocks that have cratered.

Cheap stocks often do relatively well in bear markets. In Buffett's partnership letters, he noted that when the market was increasing, he hoped to match the averages, but he anticipated the best relative results during market declines.

The Foolish bottom line
It takes courage to be a pig, but the payoffs can be excellent. In bear markets, fear can motivate people to sell great stocks for a fraction of what they're worth. Our Inside Value newsletter team is focused on cutting through all of the confusion and finding the best undervalued opportunities out there; we've already identified eight stocks trading for less than half of what we think they're worth. You can check out all of our picks with a 30-day free trial.

Fool contributor Richard Gibbons recognizes the hypocrisy of advising you to ignore hysterical headlines. He owns shares and LEAP call options on Headwaters but has no position in any of the other stocks in this article. Headwaters is a Motley Fool Rule Breakers recommendation. Washington Mutual is an Income Investor pick. The Fool has a disclosure policy.