[olufnaese]

But how do I launch an application?!

[omnicognate]

Using emacs' facilities for running child processes. I have

    ;; 's-&': Launch application
    (exwm-input-set-key (kbd "s-&")
                        (lambda (command)
                          (interactive (list (read-shell-command "$ ")))
                          (start-process-shell-command command nil command)))

Edit: There's an example configuration that has this and other bindings: https://github.com/ch11ng/exwm/wiki/Configuration-Example

[aerique]

You can use Rofi, dmenu or a similar application launcher.