To run a Fermi estimate, start by writing the question in a form that has a number for an answer, then list the factors that multiply together to produce it. For 'how many cups of coffee are drunk in a city per day', the chain might be: population, fraction who drink coffee, cups per drinker per day. None of these needs to be exact — each only needs to be right within a factor of two or three, which is a far easier target.
The final step is the one beginners skip: the sanity check. Compare the result against something you already know — total retail coffee sales, the output of a single café, a national consumption statistic. If the estimate disagrees with the anchor by more than an order of magnitude, one of the factors is badly wrong, and the chain tells you exactly where to look. That auditability is what separates an estimate from a guess.