Here's a link to an 870 owner's manual that shows full field stripping.
http://www.remington.com/pdfs/om/om_870.pdf
Just follow the manual to disassemble the gun.
There is no reason to disassemble the trigger group, and DO NOT attempt to remove the ejector from the receiver, OR the shell releases in the bottom of the receiver.
These parts are staked in place, and if removed, they require special factory tools to re-install.
The only tools you'd need are:
A fore arm wrench to allow removal of the fore arm. Unless you're replacing the fore arm there's no reason to remove it.
A screwdriver to remove the magazine spring.
A wooden golf tee.
Use this to push out the trigger guard pins. (Non-scratch).
A small Phillips screwdriver to remove the butt pad.
A large screwdriver to remove the butt stock.
Again, unless you're replacing the stock, there's no reason to remove it.
Happily, the 870 is one of the very easiest of all shotguns to disassemble. Don't disassemble farther then the manual's field stripping unless you absolutely HAVE to.