For the monitor, take the base off (it should be removable), and then you can either screw it into the shelf (maybe, depends on your comfort level with monitors, and what is exactly inside), or you can wedge it in pretty good with some wood.
As for screwing it in. Take the back of the case off and see if you can identify a few spots where you can safely screw into the case of the monitor. You will need at least 4 spots. Mark the spots, and then screw through the wood into the monitor. This is most secure if you have a couple spots on top and on the bottom.
Obviously the above would require adding a piece of wood above the monitor too. Also, DO NOT mess up, you have got to make sure that your screws will go through the plastic and hit nothing but air (or metal mounting plate).
The wood wedge method basically involved building a couple of very close walls to jam the monitor in place. This is very secure if you ALSO tie the monitor towards the back (to keep it from falling forwards). To do this properly you take the back of your monitor case off, to run your tie down materials through the case (you may or may not have to add holes), and then put the case back together.