How do I know if I can run power to a garage from my breaker box?
No need to worry, a 200 amp supply box has more than enough reserve to power your garage.  If there ever was an exess draw - anywhere in the system - your circuit breakers would react by tripping.  

You could run a sub panel to the garage, in case you ever wanted to use more powerful tools in the garage.

Install a 50 amp duael breaker in the panel, run #6 three-wire line to the garage in a plastic conduit line and connect it to a sub panel circuit box in the garage.  Then you can run individual 20 amp circuits from the sub panel to power outlets in the walls and another circiut to your workbench, etc.  you could run 3 or 4 20 amp circuits in the garage.  This would leave you in good stead for any future needs in the garage.