How many arguments (input fields) does the COUNTIF function require?

Two, the range you wish to interrogate and the criteria on which to count.

=COUNTIF(A1:F30, 3)

For example, this would count every instance of the number 3 in the A1:F30 range. (Note this is a count function not a sum function, so it is not adding them up, but simply counting how many of them are present)