While it may not be practical for everyone, downsizing to the smallest car that is practical for your family will help immensely. If you are already looking to buy a new car, there are some things you need to keep in mind.
Smaller cars are typically cheaper to insure - although you should still check with your insurance company first as some less common models of car can be surprisingly expensive to insure.
In Australia, it costs a lot less to register a four cylinder car than a six or eight, which could save a significant amount as the years pass. Smaller cars also need smaller tyres and of course they generally use less petrol.
You don't need to downgrade to a 2-seater hatchback either, you can get some very roomy cars with lots of room for the kids and their gear without needing to buy an enormous gas-guzzler.