The economy always has and always will have its ups and downs. It's easy to coast through the good times, but how do you come out of the tough times unscathed?
Talk it over. Sit down with every member of your household and go over your finances.
How you resolve and differences in your approach to money will have a profound effect on your relationship's chances of succeeding: Take a Healthy Approach to Finances in Your Relationship
Now is the perfect time to set an example of your children, and show them how a family can pull together during tough times and everyone can chip in: Teach Your Child About Budgeting and Get Adult Kids to Pay Their Share
Set financial goals. Focus on paying off debt and saving an emergency fund. If you don't already have you an adequate emergency fund set aside, specify a goal for how much money you want to add to it every month, and put an equal amount towards paying off your highest interest debt. Pay yourself first.

While normally, it's recommended that a two-income couple keep three months' worth of expenses in an emergency fund, during a downturn the recommended time is six months instead, especially if you're in an industry that gets hit hard by a recession (construction, financial services, food) and if you're a one-income family. If you're self-employed, you should set aside up to a year's worth of expenses.
Cut costs. There are a number of ways to reduce expenses.

Cut discretionary spending. Buy nothing. Resist sales pitches. Don't even think about using that new credit card offer in the mail, even if it does have a low APR and no payments for two years--evaluate it carefully. When you do need to buy things, haggle. But this is a good time, overall, to determine the difference between what you want and what you need, and reconsider your values - is your current standard of living really worth hanging onto?
Transportation - Carpool as much as you can. Consider commuting by bicycle or even living without a car. But if that's not practical, look for ways to save money on gas, even if it means hypermiling.
Housing - Get a roommate or consider relocating to an area with a lower cost of living. Maybe you can move in with family members until the economic downturn blows over. Keeping the peace in a multigenerational household isn't always easy, but it has its own rewards.
Food - Stop going out to eat; instead, try to cook at home from scratch more often. Consider the benefits of the slow food movement. If you don't have enough time to cook, try doing it just once a month. Find good deals at a local farmers' market.
Keep the money flowing in.

If you have a job, be an amazing employee. Now is not the time to slack. Show up early, stay late, and volunteer for projects. Pick up the slack for other workers; it's what will happen when people get laid off, anyway, so now is the time to prove yourself. Look for ways to save your employer money, especially if you see your employer doing little things to that effect, like encouraging employees to turn of their computers. Try to quantify your efforts in terms of how you've raised profits and cut costs. Start networking so that in case you still get laid off, you have a safety net of contacts who might be able to help.
If you own a business, develop a risk management plan if you haven't already. Find ways to reduce expenses, e.g. Virtualize Your Workforce. Improve Service Quality at Your Business so that budget-strapped customers will want to use your products or services through tough times.
If you don't have a job, find other ways to make money fast. Focus on cutting your expenses, as described in the previous step, and consider volunteering; if you've got the spare time, there are organizations that will need your help, and you could establish good karma in your community.
Enjoy life. In order to avoid recession depression, don't let fear control you; an intense feeling of paranoia can make you an inflexible employee and also strain your relationships. Be thankful for what you have, and make sure to have fun. Instead of not taking a family vacation, for example, take a Staycation or Exchange Your Home for Free Vacation Accommodation instead; invite your family to think of creative ways to save money without skimping on happiness. Accept difficult times as a challenge for your fortitude and adaptability.