What is done is the plumber or you climb up on the roof and introduce the snake into the vent stack and run it out to the street. They will then check all your drains to make sure that the system is clear.
OK, what do you do when the plumbing gets stopped up on a Friday night? You will most likely not be able to cross your legs and hold it until Monday or Tuesday when the plumber can come out at the regular rates. You could drive to the local 24 hour gas station or convenience store or Wal-mart, every time you have to go. Not a very viable option, is it? Another way to deal with the situation is to just go ahead and go and NOT flush until the plumber has taken care of the situation. Will it stink, most likely after a while it will. You could pour some vinegar into the toilet bowl. I would not use bleach as it can react with the ammonia in urine and give off a poisonous gas. Many people have died mixing chlorine bleach and ammonia together.
Other short term options include turning off the water to the toilet and flush it so that the bowl is empty and then line the toilet bowl with heavy duty trash bags –at least 2 so that there is less of a chance for the bags to leak when you take it out each day. What do you do with it then? Some people will tell you to toss it into the dumpster or to bury it. You should check your local laws as most towns have laws against discharging raw sewage.
All of these ideas can be used after an earthquake disrupts sewer services.
A longer term solution designed for dealing doggy do is to dig a hole near a tree and installing a specially made device like a bucket with an articulating cover and as you collect the dog poo and dump it in the composting bucket. A bigger solution is to take a plastic barrel such as a 55 gal water drum or plastic trash bin with a top, cut the bottom out so that it drains well cut a few holes in the sides so that worms can freely travel between the compost and the ground and they will convert it to soil, during normal times put your leaves and grass clippings in it instead of out on the curb for the city to haul off.. During ‘normal’ times most towns frown on putting human waste into something like this – check your local laws.
Longer term ideas would be to have a composting toilet. They are more expensive up front, however over the long haul you will use less water which will save you money and it will be less stress on the environment too. The compost is great for your plants too.
Most folks think that we are living longer and healthier because of ‘modern’ medical care. To an extent this is true. However, a major historical note, it was only in the late 1800s that modern man discovered the germ theory and started making use of better sanitation like flush toilets and hand washing with soap and clean water. BTW do you know where the term taking a crap came from? Thomas Crapper, the inventor of the flush toilet was knighted by the Queen, so from a literal point of view in the water closet is the crapper. ;]