The idea of unit analysis is simply to convert from one set of units to a more usful set of units. You may be working on a question that has some information in m/s and other information in km/h. Unit analysis lets us change one form of units to another set of units. Take a look at example #2 on page 10.
Unit analysis also lets us do more complex problems as well (like example #3).
The key to working with units is to ensure that you set up your numbers as fractions and include the units. Once you do this, the next coversion factor you need will be the one that reduces the previous unit in the numerator to 1 (see in example #2 how the red lines cross out the units you don't want).
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