This is one of the easier assassinations.
No fancy tricks are needed for this. You can get into his hospital simply using the scholars. Blend in the middle of them and walk towards the group massed around a large door. After the cut-scene make your way right into the hospital itself. Only use walk, don't run. Some patients will be acting mad and may slap you, just ignore them.
Garnier will be walking around the hospital on his own with no guards around him. He does occasionaly walk into and between guarded areas, but just wait for him to come back into the open, walk up to him, lock on and use your hidden blade on him. Very easy. Now you have to run away!