Looking through the viewfinder or on the top LCD there is an exposure scale whenever we are in M mode or whenever we have applied exposure compensation in A,S, or P modes.
Lets take the snow example, the camera's metering system will try to render the snow as medium gray. We must therefore override the camera's metering system. Lets say by decreasing the shutter speed by one stop.
First in A mode we would use positive exposure compensation of one stop. When we take the picture the shutter speed would have been decreased by one stop (assuming manual ISO). Before the exposure compensation was added no exposure bar would be visible. After the exposure compensation is added the exposure bar appears, and will show one stop of compensation.
Second in M mode we would simply change the shutter speed by one stop. The exposure bar (which is always visible in manual mode) will show that the camera thinks we are one stop overexposed.
Third in M mode we could use one stop of exposure compensation. If we keep the original exposure, the exposure bar will show that the camera now thinks that our shot is one stop underexposed. Once we zero out the meter by decreasing shutter speed one stop we will find we have done the same thing we did in the second case above.
We do not have to use exposure tables in manual mode, just look at the exposure bar. That tells you what the camera would have picked in A mode.