The use of the stylus depends on the particular application--the stylus itself does nothing unless an application/software makes use of it.
Having said that, in Windows and many programs, you typically can select with it (just like with your finger, but with more precision) and right-click with it (to right-click, press its bottom button and click on the screen; or hold the stylus on the screen (no button press) just like you would do with your finger).
Writing programs that use the stylus include Windows Journal and Microsoft OneNote. And drawing programs include Paint and the FreshPaint app. Try them out and experiment with the menu options.
As to the stylus' operation, it turns on and shuts down (after a small bit of inactivity) automatically, based on proximity (or not) to the tablet (and, I think, it will stay on if the tablet is in connected standby as opposed to a full off)--and so you may want to keep the stylus away from an "on" tablet if you're not using the stylus, to avoid battery depletion. There is no manual on/off button. And the function of the stylus' buttons again depends on the app/software--in Windows, when the bottom button is pressed and you click the screen, you get a right-click; and in some drawing/writing programs (such as Journal), the top button, when held, will switch on an erase function. I'm afraid you'll need to experiment a bit--but, there are only 2 buttons. 😉
Perhaps those with more than my scant experience can offer more detailed help. But perhaps this gives you a start! 🙂