Shining Star for All to See
Star Day is, as the headline suggests, better celebrated tonight as Star Night. This is the common, acceptable practice.
Hopefully the skies will be clear enough tonight that you can celebrate properly.
"What is properly?" you ask.
I can't tell you exactly how to commemorate this day/night, but I can tell what not to do.
Don't worship the stars or any other heavenly bodies. Don't fall into the trap of astrology (astronomy is fine - don't confuse the two) which any rational person realizes is hooey anyway.
Other than that, pretty much anything legal goes.
It's good that this special day comes in early September before it gets too cold in the evening, unless you're way, way up north.
Grab your binoculars and/or telescope and go outside for a while tonight. If you don't own a pair of binos (as they're often called by the experienced) or have a telescope, let me know. I'll send you to a site called Optics Owl that reviews them. (I do have a special interest in that site.)