The above picture is of my waste set up. The three bags on the wall are made of cloth. I used cotton to make them, you can buy cloth laundry bags if you're not into sewing. If you do make your own, I suggest doubling up your seams.
These work well and they are washable. I have three, but your family may need up to five, depending on the rules of your nearest recycling center and your household habits. In my city, there are many recycling stations throughout, placed in parking lots that are free for public use. I have a trash service station two miles from my home that accepts all of my recyclables. The bags on the walls are for cardboard (like cereal or cracker boxes), plastic and metal. We save and reuse our glass containers, and office/news paper. The larger trash bin is for garbage, and the small is for compost. I have a good sized composter out back.
On our "trash day", which is any day we choose, we just grab up our four bags and put them in the car. We dump the recyclables into their allotted bins at the recycling center, and on our way home, we drop by the car wash. There, we will clean out any debris in the car, including our small bag of trash. Just so we're not being blatantly dishonest and "dumping" our trash, we take some time to vacuum out the car and wash it. Once a month or so, I wash the bags before hanging them back up.
That's pretty much the nuts and bolts, but this system would not work if we did not have a few very particular trash rules.
This really encompasses a lot. From being mindful of how items we purchase are packaged, and opting to buy items with less waste surrounding them - to not hauling home junk from a yard sale that we're not completely sure we would use. When you don't have the convenience of setting unwanted things out by the curb and having them hauled off, you become much more aware of that fact that everything you use will wind up being disposed of in some way. This can help your wallet as well as your wastefulness, as you tend to stop and consider how much you really "need" something before you buy it - and whether or not that need is worth the inconvenience of the disposal.
Don't create trash.
In my household, we forgo any items whose sole purpose is to become trash. Paper towels, napkins, baby wipes, disposable dishes, tissues, etc. The only exception is toilet paper. Instead, we opt for tea towels, bandannas (which are used as hankies and cloth napkins), cloth diapers and wipes, etc. And Swiffer? That's pretty much a swear word in my book. By using cloth items and simply washing them, we not only save on our amount of waste for our budget and the planet, but we never have to worry about running out.
If it's useful - in ANY way - it is not trash
This does not make us hoarders, see rule one. Those plastic yogurt containers? They make awesome reusable Dixie cups! And sour cream and dip bowls are perfect cereal bowls for little ones because they're so much harder to tip. Whenever we have an item to throw away, no matter how large or how small, we will take a few moments to give some creative thought to the matter. Can this be reused for another purpose than what it is typically used for? Can it be turned into something else with a few alterations? What can I do to avoid throwing this into the trash? Not only are we less wasteful because we are not throwing as much away, but we are saving money by needing to buy less. The bottom line is, we only send things to the landfill when we must.
Anything that biodegrades without leaving harmful byproducts goes into my handy dandy composter. If you don't have one, don't sweat it. They are so easy to make! You can use an old trash container, laundry hamper, or any kind of bin. You can even make an enclosure out of just about any kind of fencing materials. If you google it, you will find it.
Food is not trash
I pride myself on being a relatively calm person. However, you do not want to be at my house on a day when someone puts food (or my saved food containers) into the trash. Mainly, it stinks. If I am going to have but one bag for trash for the whole week and it sits in my kitchen from Monday to next Monday, then the spaghetti that was thrown away on Tuesday is going to reek up my entire house by Friday at the latest. And Daddy will not thank you for stinking up the car come trash day. Everything that goes into the trash or the recycling bins must be rinsed clean of any food or anything that will cause odor. So when it comes to food: Eat it. If it can't be eaten, compost it. If it can't be composted, it goes into that garbage disposal I spent over a hundred dollars for. If it can't go down there (this means animal bones and shrimp tales), it goes into the freezer to be used to make stock. Then it goes back into the freezer to be refrozen, and only then it will be taken out on trash day.
This may seem like a lot. Having to sort, rinse, think about and transport waste (not to mention washing boogery hankies and poopie diapers). But they say it only takes three weeks for a new practice to become a habit. My family and I do these things without giving them any thought. Which makes for odd moments when you're say, visiting a friends house and they ask you to throw away a plastic baggie that is COVERED in food and you find yourself trying not to argue with them about the fact that it needs rinsing first!
Ultimately, these changes can give back huge rewards. Your wallet, in that you're buying less by wasting less in the first place - the 60$ to 100$ per month that you are NOT paying the trash guys (sorry trash guys!) and the environmental impact you are having on so many levels.