You can't be on reserve and see an uncovered trip and pick it up. CS assigns trips the day before or the day of the trip.
You can volunteer to fly on your days off (OG= 1.0 pay, Premium reserve PR =1.5x pay). OG and PR get added to your guarantee for any trip that touches any of your days off*. You don't get to choose to pick up a trip, instead CS calls you the day before while filling open time and offers it to you if they're out of reserve coverage.
* - The perfect OG/PR trip is one that barely touches your day off and is mostly work when you were going to be on call anyway.