It took me a while to find this when I first used a phpBB, so don't feel bad.
I think you have to "edit" the first post in the thread. Kind of towards the bottom there is a set of radio buttons like this:
Post topic as: o Normal o Sticky o Announcement
Click on "Sticky" and save.
And yes, you can either give a single person the ability to make posts sticky by forum or you can create a group that has customized permissions by forum. You could also make them a moderator in a forum because that includes the ability to sticky posts (but includes other privileges as well).
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