You can use Astropad with your finger, just as you would with any touchscreen iPad app, but a stylus is better. Astropad supports multiple pressure-sensitive pens, so if you already have one of those for your iPad, you can likely use it with the app.
Keep in mind that Astropad itself is really the mechanism to turn the iPad into a graphics tablet; it doesn’t replace graphics apps such as Photoshop for content creation. Instead, it enables the iPad as an interface for such apps.