If you are not familiar with what the speedometer cable looks like, unscrew the connector nut on the cable sleeve where it connects to the speedometer drive down at the axle. The speedometer cable inside the sleeve is made like a long thin spring so that it can flex.
I can think of a couple of ways to attempt to repair a broken cable temporarily in an emergency, but I can't think of an emergency that would make me want to do that.
The best solution is a new inner cable. If it would take a week to get the cable and I had to have a speedometer tomorrow, I would get a $15 bicycle speedometer from Walmart. When the cable came in, I would give the bike speedometer to some kid.