What should I do when a (house's main) sewer backs up? How can I make it not back up, or at least stop it from backing up more once it has already started backing up?
You have a couple of options.
If this does not happen often, you can likely put a stopper in the drains which backup in the house, and just wait until the sewer is no longer clogged. To do this, you can purchase a "test plug" for each drain that is experiencing the backup (if you also get backup in a toilet, you will need to pull the toilet to install the plug). Of course, the downside of this approach is that you need to be at home when the backup occurs, and you need to go through the hassle of plugging the drains / pulling toilets / etc every time it happens.
If you want a more permanent solution, you can install a backflow prevention valve on your sewer lateral. This will likely involve digging up your yard, splicing the lateral, and installing the valve. With this option, you do not need to be present to prevent the sewer backup. However, this will essentially block off your sewer lateral until the sewer stops backing up. This may cause some backup in your house (if, for instance, you take a shower while the backflow preventer is tripped).