You basically look at the vertical scale and the horizontal scale and convert them to the same unit of measurement. Metres is usually the best one.
e.g. vertical scale - 1:50m
horizontal scale - 1:100 000 (the horizontal scale would always be in centimetres at first as marked on the map)
Convert them to the same unit of measurement and this would make
vertical scale - 1:50m
horizontal scale - 1: 1000m
Step 2: Then you just divide the metres of the horizontal scale by the metres of the vertical scale.
1000m divided by 50m = 20
i.e. The vertical exaggeration is 20.
Just remember that when you're trying to calculate the vertical exaggeration on a topographic map, it won't always be a whole number so you'll be expected to round it to the nearest one.