How do you remove a spark plug that broke off in the car- there's nothing sticking out and we actually broke the tool we used to try to remove it- we can't afford to take it to a shop- what now?

Spark plugs have hex shoulders to use with socket tools. It would be near impossible to break the threaded shaft or hex off the plug.

Assuming the porcelain top is what broke, you still need to use a socket to remove the remainder of the plug. If it is cross threaded, go to a parts store and get a thread chaser to clean the threads before trying another plug.

The thing is, if the threads are crossed you will drop some filings into the cylinder. unless you can get everything out of the cylinder it will damage the walls causing ring failure or piston or valve damage. Many cars have alum heads so filings will not stick to a magnet.

I suggest you follow steps above and use a shop vac with narrow tip to vacuum out the cylinder before cranking the engine. It's the best a do it yourselfer can do but it's a risk.