What are RSO (Range Safety) duties like???

Your unit and or the range control office will have a detailed SOP and duty description.
Your best bet is to look at both to satisfy your info needs.. as failing to follow either documented responsibilities will result in the same thing,,, a failed range experience either because you failed to follow unit SOP, or because you failed to follow range controls SOP and the event never happened.

As an or the RSO, you are tasked with the actual running of the firing line and the areas around it, as the OIC will likely be in the tower.

You will create and enforce firing orders (if not already done), select NCOs for safeties, and above all, ensure the general safety of the firing line and firers.

It's not tough, just a lot of attention to detail and being able to track several people and events going on at once.

Good Luck!

No sooner did I read yr question than I came across this link which gave even more meaning and significance to your question. As others have said read and know the range safety regs and follow them to a T., talk to someone else who was a RSO at the same range for insights to potential problems; make sure your comm is working to Base Range Control, the tower and anyone else. Coordinate in advance with the senior range NCO, get there early if possible and start checking things out. Make sure you get a good count of ammo you sign for, before and after, as well as any weapons you are responsible for checked out from the armory in y our name.
http://www.usatoday.com/story/news/nation-now/2016/05/11/soldier-killed-live-fire-training-la/84252554/