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The computation of a Bacon number for actor X is a "shortest path" algorithm, applied to the co-stardom network:

Kevin Bacon himself has a Bacon number of 0.
Those actors who have worked directly with Kevin Bacon have a Bacon number of 1.
If the lowest Bacon number of any actor with whom X has appeared in any movie is N, X's Bacon number is N+1.

Here is an example, using Elvis Presley:

Elvis Presley was in Change of Habit (1969) with Edward Asner
Edward Asner was in JFK (1991) with Kevin Bacon
Therefore, Asner has a Bacon number of 1, and Presley (who never appeared in a film with Bacon) has a Bacon number of 2.

Here is another example, using Sir Ian McKellen:

Ian McKellen was in X-Men: Days of Future Past (2014) with Michael Fassbender and James McAvoy
McAvoy and Fassbender were in X-Men: First Class (2011) with Kevin Bacon
Therefore, McAvoy and Fassbender have Bacon numbers of 1, and McKellen has a Bacon number of 2.

Because some people have both a finite Bacon and a finite Erdős number because of acting and publications, there are a rare few who have a finite Erdős–Bacon number, which is defined as the sum of a person's independent Erdős and Bacon numbers.