Harry -- you guys don't exactly inspire confidence, just based on the
way you are talking. But you also don't sound like guys that are going
to go hire an electrician either.
So please, take som extra precautions when doing this kind of work:
- Turn OFF the circuit breakers at the main panel. No one should ever
be touching any wires or anything when the power is on (even if you
turn off the light switches).
- Be careful that no one mistakenly turns on the circuit breaker when
anyone is near the opened wire boxes.
- Just to be sure everything is off, test the wires for power (try
combination of whites, blacks, bare grounds, the box itself, etc.),
using a handheld voltmeter. If you don't have one of those, carefully
make connections between wires using the metal of a screwdriver while
being very sure to hold only the plastic insulated handle. If you see
any tiny (or huge) sparks, stop.
- When making connections, make sure the wires are tightened down
firmly, but don't tighten so much that you crush the wire or begin to
strip the screws.

BTW -- you really are not supposed to put two wires on the screw
connections like that. They were not designed for it. BUT, maybe you
would be best off just leaving it, instead of risking making it worse.
The correct way would have been to get a short piece (about 5 inches)
of the correct size wire, called a pigtail, stripped about a half inch
on each end. The ends of the two wires, plus the pigtail, are carefully
twisted together, then a plastic "wire nut" screwed on to the bundle to
cover up the exposed wire. The other end of the pigtail now gets
connected to the screw on the switch.

In any case: make sure you don't have any loose connections, and make
sure that any exposed, stripped wire isn't going to touch anything
inside the box by mistake. Exposed ends, if any, should have a wire nut
on them. And for the screw connections, only strip enough of the wire
to make the connection, no more.