There are lots of Green runs at Monarch. It is easy to find your way around the Mountain using Sleepy Hollow and Lower Tango. But, if you want the BEST and easiest route down the mountain, that has to be SkyWalker to Sleepy Hollow to Glade.
This is probably not a good idea for your first day on a snowboard, but once you feel comfortable riding the lift, can do front side and back side turns, and have an idea how Monarch Mountain is laid out, give it ride.
From the Monarch Base Area, take Tumbellina all the way to the top. Head straight ahead onto Rookie, this turns right and leads over to the Panorama Lift. Load onto Panorama (note that this chair moves much faster than Tumbellina, so get into position with alacrity).
Once you unload at the top of Panorama, head left and clear the lift unloading area. Look around, enjoy the view. Skywalker is a pretty flat ride all along the top of the Monarch Ridge. This is also the Continental divide, water to your left goes to the Atlantic, and water to the right goes to the Pacific. Keep your speed along the run. You can peek over the edge and be glad you are not heading down Mirage or Turbo!
Skywalker takes you all the way down the ridge, bends left and meets up with Sleepy Hollow (to the right). This green route is a great long run on a cat track and then mellow, open runs. Stay to the edges of the run for the best snow. Sleepy Hollow will eventually drop into Tenderfoot and Glade, both good choices. Make sure to look uphill when you come under Pano, lots of other runs converge here, and it can get crowded.