Don't clean it or lube it, just shuck it till you hurt, for about 10 days. Dry fire to your hearts content, won't hurt a thing. Then clean it, and don't lube it. Shoot the snot out of it, and don't clean or lube it, shoot the snot out of it some more. Within 10K rounds of this it will operate as if made of glass. Personally I never lube my 870. Anytime I have lubed it I have had trouble, as in sub 0 weather it gets stiff, or after 4 or 5K rounds it gets stiff. I shoot mine dry, just enough oil to keep the rust at bay and that is it.
I know some guys that have used non-embedding lapping compound to smooth an 870 out, but I have found that shooting the snot out of it makes a guy a much better shot than the guys with the slick new 870s.