How to find number of fonts in InDesign?

The other thing you can do is create a Report through the Package command... that will include a list of the used fonts and file paths.

Some font managers have a utility to check the font usage in various document formats. including InDesign. Although they can be mislead by unused Styles, etc, to list many more fonts than actually used, this would be the same issue you would face using the Find / Change Font route... as it also reads fonts defined in Paragraph and/or Character Styles, whether you use them or not.

Package?

The keyboard shortcut to this is Alt F on a PC, not sure what it is on Mac, maybe Opt F

Check out this script. You can assign a shortcut to it.

I'll add two more things to what Bob has said:

In current versions of InDesign, the command is Type > Find/Replace Font.

You can gain much more information in the dialog of you click the More Info button when you have a font selected in the list.

Then you can see a large amount of information of the font - how many characters or styles are used by the font, what type and version, and so on as shown below:

Type > Find / Change Font