The draft starts at 6pm Central time--you can watch on the MLB Channel or online (I think its free). 

I think there are 5 minutes between picks--so the Royals will be picking around 6:15ish depending on how much Selig opening remarks crap there is. 

Only the 1st Round and Supplemental Round tonight--50 picks total.  After the Royals pick the big thing to watch is who might slip to the Royals in the 2nd Round tomorrow--they have the 54th pick.