Determine a container, a location, and let everyone know where they are
An emergency kit is only as good as the box that contains it, and only useful if people can find it in the event of an emergency. A sturdy, waterproof canvas bag is a great start. Ensure it has a handle so that it can be moved if needed, and make sure it's strong enough to hold everything inside it. Make sure it's kept in a place where everyone in your family knows how to find it and that everyone can reach it.
Stock it with Food and Water
The most important long-term item in a disaster is likely water, followed by food. You can survive a long time on non-perishable items, such as canned goods, peanut butter, energy bars, dried fruit, and so on. Just make sure you include a can opener! But you'll be seeking water very quickly. Be sure and keep one gallon of water per person per day.
Safety and Communications
If something goes wrong, you'll want to find out what's happening. A cell phone/radio with extra batteries (or one that is crank-powered) will keep you informed. A flashlight will let you move around if needed. Blankets will keep you warm and a first aid kit will help with minor injuries and illness.
Review and Restock Annually
Thankfully, there's a good chance that you'll never have to use your emergency prepardness kit. But if you do, you'll be glad that each year you take time to make sure that nothing has expired or needs to be replaced. A good day to do this is on your birthday. You're already feeling thankful that day, so taking a few minutes to ensure that you are prepared will help make the rest of the day even more pleasant.
Home Emergency Kit Essentials (via ready.gov)
Car Emergency Kit Essentials (via edmunds.com)