I see three ways to accomplish a starry night sky.  The first and simplest way is to use one or more starry night Gobos and project them onto a cyclorama or plain colored back drop.

Stage Directions magazine had a very detailed article on making a starry night sky about a year ago.  It involved using a durable black curtain and cutting small slits in it where ever you want a star to be.  Then poke small Christmas lights through the holes from the back and light.  Anyway that seemed to be the "jist" of it.  I am sure there are subtle intricacies involved that I am not conveying here.

Word of warning: A theater I've worked with in the past made a starry night sky out of their upstage black curtain by poking Christmas lights through it. They figured, once the show was over, they could re-use the curtain by just pulling the lights out and nobody would notice the tiny holes left in place.

Unfortunately, to secure the lights to the back of the curtain, they used duct tape. Every time they pulled out a light, the tape pulled the backing of the curtain away, leaving large, faded spots that were VERY noticeable.

Since they could not afford to replace the curtain and before the curtain could be ruined entirely, they stopped pulling the lights and left them in place. Now they have a permanent set-up for a starry sky whenever they need it.