they had to run around everywhere.

1. the form of the verb that comes after "had" is the base form. in this case, "to run" is the base form.
2. the negative form of "had" is "had not" or "hadn't".

he didn't have to go to a public spa.

1. the form of the verb that comes after "have" (in the negative form) is the base form. in this case, "to go" is the base form.
2. the negative form of "had" in this sentence is "didn't have" or "did not have".