Congratulations- use it in good health.
DEFINITELY clean it before you shoot it. Especially the barrel/bore/chamber. Remington coats new guns with a preservative before they leave the factory. If you leave the stuff in the chamber it can in some cases help cause fired hulls to stick, and cause difficult extraction. Sometimes on rare occasions hulls will stick even in a clean chamber, and changing ammunition brands is the solution to that one.
870s are among the easiest repeating shotguns available to field strip and clean. The directions are in the owners manual. Learn how to do it, and get familiar with how your shotgun works. Learn to manipulate the gun properly by reading the owners manual before you ever put the first shell in it.
First thing to do as far as shooting is concerned is to determine which eye is your master eye, and make sure your master eye and your 'handedness' are on the same side. Make a circle with your fingers and thumb on one hand, hold your hand out at arms length with both eyes open, and center a small object (doorknob etc) in the circle. Close one eye, then the other, alternating left-right. The eye that's open when the object is still centered in the circle is your master eye, and ideally you should shoot from that side also.
Remember- safety first. It's a bad thing to have an accident with any firearm, but shotguns at close range can be tremendously destructive. Be careful.
Start out with light birdshot loads as you're learning, 7/8 ounce or 1 ounce shot loads are likely to kick less. Learn the basics of gun mount, get someone to teach you if you have no experience at all. Proper form will do a lot to reduce the punishment of recoil.
Now, go wear it out- dare you!
lpl/nc