Does anyone know how to show the count of the results of a custom view?
You can add a custom section to either the header or footer to do this.
Edit the view / display.
In the center section, click Add next to Header or Footer.
Choose Global: Result Summary. Add it where you need it.
Then, edit the textarea to be the format that you need. There are a bunch of tokens available for building up the numbers.
Preview the view, and then Save if everything is OK.