It's a rare family that doesn't have a surprise expense pop up now and then—and sometimes that bill can be a big one. Here's how to prepare.

More than half of Americans had a major unexpected expense last year, according to a recent Bankrate survey. But only four out of 10 of them have the money in savings to cover a surprise bill. That's a precarious position to be in, especially for new parents, but bulking up your rainy day savings doesn't have to be a headache. In fact, a few small changes can create a cushion that will carry you through a variety of storms. Here's where to start:

Save to a separate account.

Keeping emergency savings in your checking account is an invitation to spend the money. Instead, choose a separate savings account—preferably one earning some interest. "You can get the funds within a day or two, but they're out of sight and out of mind," says Dina Megretskaia, a financial planner in New Hope, Pennsylvania. "You're less likely to use them up before an unforeseen financial need strikes."

Automate your savings.

Not sure where to start? Consider having some amount of money automatically transferred from checking to savings on paydays. Like 401(k) contributions, that means the money is gone before you even see it, and you don't have to choose to save each month—it will happen for you. "It can be really hard to save money," Megretskaia says. "It's easy to think, 'I have this need or desire right now,' and it's hard to put money away." Start small if you must—$50 or $100 a month if that's all you can spare. The important thing is to get started.

Aim for three to six months of expenses—but think it through.

The rule of thumb is that you should try to have three to six months of expenses in your emergency savings, but you may need more or less, depending on your circumstances. For instance, are there two earners in the family at two different jobs, or only one earner, making you more vulnerable if that person loses a job? You may want to put more away. How much of your income is going toward needs and how much toward wants? "If you have a buffer in your budget, and you can live on less, that gives you flexibility," Megretskaia says.

Put away your tax refund.

If you're getting a big check in April, funnel it toward your emergency fund. "It's money that people don't really think of as theirs," Megretskaia says. "So it's easy to say, 'Let me put it into savings.'"

Save to a Roth IRA.

If you're eligible for a Roth, and you already have a few months of money in a liquid savings account, consider saving extra emergency money here instead. "This account is special when it comes to tax treatment, and has the advantage that at any time, you can take out the money you contributed with no penalties, for any reason," Megretskaia says. That means you can save for retirement, but if you need the cash in a pinch, you can still access it.

Preserve your social capital.

Money isn't the only thing that can get you through a tight spot. Friends and family can also be crucial to your survival, so make sure you're keeping up connections. "If you don't have grandparents or family to lean on, building a community of folks who can lend a hand by cooking a meal or looking after a child will make your life better and richer, especially when you face stressful or unanticipated situations," Megretskaia says.