The clippers themselves don't need much care, it's the blades themselves. Just keep the loose hair cleaned away from the clippers, underneath the blades, keep any liquids out of it, and don't wrap the cord around the clipper body, just coil it loosely. Otherwise the cord weakens inside the sheath
Brand new blades need to be cleaned with a blade wash, and oiled, as they have a protective film on them, if you don't clean this off they won't perform well. Blades need to be cleaned and oiled after every use.
Here is an excellent website with instructions and photos for clipper and blade care:
http://thebladeguyz.com/clipperbladearticles.html
