Ok, I am a new inexperienced home owner with a cracked sewer pipe. It is cracked in the basement where it connects to the one that leads into the ground outside. How does one fix this?

First tell us what material this pipe is: Cast Iron, PVC, ABS, Clay ?
Than find out what diameter it is. You will have to cut out small section of the broken pipe and replace it with new piece of pipe. You will connect new and old with Fernco shielded couplings.

Iron pipe