To get a plate from a clockwork soldier, you first have to destroy/kill the soldier. After it's dead, search the scattered pieces on the ground to find and pick up the plate. Your first chance to complete this will be in the Clockwork Mansion mission, where there are plenty of clockworks soldiers to eliminate (if you wish).
The soldiers are harder to take out than a normal enemy. You can't really sneak up behind them without them detecting you. You can drop assassinate them with some success, but even that won't take one out (the first time you drop on one, it will remove their head, which eliminates their ability to detect you, if not actually killing them). I believe you have to hit them with the equivalent of two or three killing blows to completely eliminate them. Also, when they are about to die they explode, so you need to get away to avoid potentially fatal damage if you're close to death yourself.