There are two ways to go about the process of having a dog waste composter/septic system in your back yard. One way is to make one yourself and the other is to buy a product like the Doggie Dooley, which comes in several different sizs based on the amount of dogs you have.
There are some really basic steps to building your own that I have found on many websites and they are all the same:
1. Take and old garbage can and drill a dozen or so holes in the side.
2. Cut out the bottom (A keyhole saw works great for this.)
3. Dig a hole in the ground, deep enough for the garbage can.
4. Toss some rocks or gravel in the hole for drainage and position the garbage can so it's a little higher than the soil level.
5. Place the lid on top (you might want to paint it with something like Dog Waste Composter.)
6. When you scoop some poop, put it in the hole and sprinkle in some septic starter (available at hardware stores) and add some water.
They typically take about 24-48 hours to start to break down and from there you can add daily and it should hold it's own. You also want to consider the location for this contraption. Don't put it close to a garden or in a wetland, also keep it away from any water sources if you are on a well system. Outside of that, once you get the thing started, it's no more plastic bags or smelly garbage cans.
The second product the Doggie Dooley comes in different sizes. The 3000 that I talk about here is for 2 large dogs, that's what I have. Basically it's all set to go, you just need to dig the hole, add water and septic powder and you have you system ready to go.
From what I have read and what I have seen it sounds like the septic bacteria is environmentally safe, so you really aren't harming anything, just make sure it's not near food sources or water sources. You still don't want environmentally friendly bacteria to get into your food and water. It may not be bad for the environment, but not so good for you.
Just think of all the plastic bags you will no longer be using and the garbage guy will be happy that when he opens your cans, they won't stink horribly anymore.
Do your part and start with simple solutions