Most proper mobo standoffs these days are either metal (w/ male and female threaded ends) or like spring metal that snaps into square holes in the mobo pan. You take a proper sized screw and fasten the mobo to the top of the standoff with it. Very few if any use plastic standoffs any more. I use the ones I have left from back in the day and use them for extra support around the card slots and memory sockets if there are any available holes in the mobo.
. What is the make and model of your case? The manual that came with it should show what type of standoff it uses and how to use it (if it's not obvious).
.bh.
PS: Look a the new builders' guide at
http://www.Mechbgon.com - has most common standoffs covered. There are other types he doesn't show, but those are the most common. Do a Web search on- motherboard standoffs -to see more types. .bh.