Today as I was pulling out my garage in reverse, the car made a loud clunk like I backed into something. When I applied the brakes, the car started shaking and vibrating like crazy. I mean, the interior, dash and steering wheel were all shaking voilently.

Could this be an engine mount or transmission related problem? I haven't noticed any problems with shifting gears but I have noticed the vibrations say at a stop light.

Is there a transmission fluid reservoir or dip stick that I can check my tranny fluid level? I looked and didn't see anything visable.

 

Well I'm guessing you have an auto tranny.... I would GUESS that it is an engine mount. You can check the oil. It should be near the battery. If you have a manual tranny, do this:
Take out battery
Take out battery tray.
Look towards the firewall for a sensor on a plug. With a 10mm socket, loosen the screw and take out the plug. Depending on the level it should mark over the teeth on the pinion.

 

Yes, I have an auto transmission. I checked the fluid level and it's fine.

Next service, I'll get the engine mounts looked at.