Having an emergency fund is one of the smartest moves you can make, especially if you're a single income family. A good emergency fund can make the difference between coping financially with what life throws at you and having money stress adding to the problem.
If you're on a tight budget, as many stay at home moms are, it's hard to start an emergency fund. If at all possible, take $30-50 a month and put it into a special account that is just for emergencies. If you can't pay that much, even $10 a month will help.
This money must stay in an account that you can access easily, such as a basic savings account rather than a CD. You don't want to have a waiting period to get your money when you have an urgent need. At the same time, you don't want to access it casually, although that should be more a matter of self control.
How big your emergency fund should be depends on what you're likely to need it for. You'll need more of a stash if you know you have a major appliance getting ready to go, or if you car tends to need a lot of repairs or someone in the family has a lot of health issues. The equivalent of two months' salary may not be a bad idea, as that can cover a lot of ground.
Make sure that you're good about using your emergency fund only when you have to, and that you pay back into the fund as soon as possible. Better to have to pay back yourself than to pay back a credit card company with interest.