You need to take the caps off of the scope and there will be a slot where you can insert a screwdriver (or a penny) to turn the adjustment screws. The cap on the top will adjust windage and the one on the side will adjust elevation. There should be something there that says "1 click=1/4 inch at 100 yards" and a + and - on there too (if you turn the screw towards the + you will increase elevation and towards the - will decrease.) At 50 yards each click will be HALF of what the interval is at 100 yards. So 1/4 inch at 100 yards = 1/8 inch at 50 yards.
Anyhow, you NEED to go out and sight it in. Shoot a 3 shot grouping first to see where you are. If you are 4 inches low at 50 yards try to turn the elevation adjustment up about 20 clicks or so (depending on the adjustment interval on your scope) and shoot another 3 shot grouping to see where it is, and keep adjusting from there. If it is still off then adjust accordingly. The KEY is to shoot a THREE shot grouping (not one) after making your adjustment to see where you are at. One shot will not do because you need to find the average of where it is set (and you will flinch). I know this is painful but if you want to shoot straight this is a must. There is no excuse for having your gun out of adjustment.
Another thing to consider:
What ammo are you shooting? Are you shooting with your bird barrel? I ran a Remington 11-87 with a Remington fully rifled slug barrel and a 2.5x scope and could shoot 1 inch groupings at 50 yards with Federal sabot slugs. It is worth the extra $$$ to invest in a good barrel or even a rifled choke tube if your 870 has the REM-Choke.
Also:
Where do you want the gun to shoot? Dead on at 50 yards.....75 yards? You can adjust for range like this if you know the ballistics of the load you are shooting. I.E. You can sight in at 80 yards and know that at 50 yards you will be 3 inches high. This may apply to rifles more that shotguns. I have my 22-250 sighted in for 200 yards for varmints. I know that at 100 yards I will be 2 inches (hypothetical) high and at 300 yards I will be 2 inches (hypothetical again) low. So I adjust my point of aim from there (really hypothetical now). I reload so I know what the ballistics of each load is so I can extrapolate the drop at 300 yards and confirm it when I sight it in. Is that too much? Let me know how it goes. Good luck.
Anyhow, you NEED to go out and sight it in. Shoot a 3 shot grouping first to see where you are. If you are 4 inches low at 50 yards try to turn the elevation adjustment up about 20 clicks or so (depending on the adjustment interval on your scope) and shoot another 3 shot grouping to see where it is, and keep adjusting from there. If it is still off then adjust accordingly. The KEY is to shoot a THREE shot grouping (not one) after making your adjustment to see where you are at. One shot will not do because you need to find the average of where it is set (and you will flinch). I know this is painful but if you want to shoot straight this is a must. There is no excuse for having your gun out of adjustment.
Another thing to consider:
What ammo are you shooting? Are you shooting with your bird barrel? I ran a Remington 11-87 with a Remington fully rifled slug barrel and a 2.5x scope and could shoot 1 inch groupings at 50 yards with Federal sabot slugs. It is worth the extra $$$ to invest in a good barrel or even a rifled choke tube if your 870 has the REM-Choke.
Also:
Where do you want the gun to shoot? Dead on at 50 yards.....75 yards? You can adjust for range like this if you know the ballistics of the load you are shooting. I.E. You can sight in at 80 yards and know that at 50 yards you will be 3 inches high. This may apply to rifles more that shotguns. I have my 22-250 sighted in for 200 yards for varmints. I know that at 100 yards I will be 2 inches (hypothetical) high and at 300 yards I will be 2 inches (hypothetical again) low. So I adjust my point of aim from there (really hypothetical now). I reload so I know what the ballistics of each load is so I can extrapolate the drop at 300 yards and confirm it when I sight it in. Is that too much? Let me know how it goes. Good luck.