How do you make 13 with four 4s?

Three fours and one half of 4

Or if you mean using only fours and operation signs you develop methods like this:

42 - 4 + (4/4) = 13.

In Words, four squared (16) take 4 (12), + the sum of 4/4, which is one (13).

Obviously, being an Prime number, 13 doesn't fit equally into four, so use a combination of different mathematical symbols to change four into many other numbers:

42 = 16

Square Root of four = 2

4! (four factorial) = 24

43 = 64

4/4 = 1

4 + 4 = 8

Combinations of these can be used to make the 13 you're after.