well welcome to the site
first off, there is NO sure way to kill a deer, there wild animals and can move and have there own set of survival skills and tools to get away from those trying to hunt/hunt/kill them

so you need to use the skills you have to try and out with there, thus why its called hunting and NOT shooting!

NEXT< before you go and place any food, leftovers or BAIT as its called by the law, you need to make sure its legal
or you can be breaking some laws and asking to get a fine and loose your hunting licence as well!

every yr you HAVE to buy a lic and have proper tags per animal/season you wish to hunt in also
so, making your your legal is a BIG part of hunting

as for your shotgun, a rem 870, they can be drilled and tapped to add a scope, to help you be even more accurate
shooting 2-3/4 inch slugs over 3 inch one's will also, help tame some of the recoil on your shoulder too!
make sure when your shooting slugs you NOT shooting them thru a choke any tighter than a modified choke(the type of choke that screws into the barrel, your gun should have removable one's if of modern era, and if NOT, on the barrel it should state the FIXED Choke size it in, too tight a choke can be dangerous when shooting slugs!
they actually sell, SCREW in chokes that are rifled to help make slugs fly better out of smooth bore shotguns!
they also sell rifled barrels that fit your gun and are very easy to add to make it a much more accurate gun(but yes there is costs to this, not a LOT but some)

when hunting deer, the name of the game in most places is finding where they sleep/eat and drink
and then setting up sopme where in between them, waiting ,
be it waiting between a bedding area(what its called where they sleep) and a food source, this is maybe the most common method for evening hunts and morning hunts
evenings your waiting for them to pass GOING to food, and mornings, your waiting for them to go from food to bedding area!

some folks like to STALK There game, but this is a lot harder and takes slow goings and some skills to be more alert than the game your after
as spotting them before they spot you can very VERY hard as they tend to have better ears, nose and eyes than most humans!
yes some folks get good at this form of hunting, but many don't
and tend to rely on luck, that a deer will many times STOP and look back after running a short distance and allowing for a shot!

but by far IMO< sitting between food and bedding area's are the most common ways of whitetail deer hunters
be it setting up a treestand , or a deer blind, be it man made commercial like type, or made of things in the area
being where DEER want to be,m before they get there is the name of the game

ADDING< BAIT, again when legal can help lure deer into places and allow for you to get a deer, BUT many times adding bait, teaches deer that food is there at NIGHT also, and most bait sites in any place that has hunting pressure, many deer will ONLY use at night

spending time in the woods is a great way to learn how to find deer, where they are, where they go, what they eat, where they sleep
following deer SIGN< be it tracks, droppings, rubs on tree's scrapes, main worn in ground trails and so on

hunting is a SKILL< the more time you spend in the outdoors paying attention to things, the more time you TRY to learn things, the better you can get
there is no magic pill or words, that make up for experience and time learning
I grew up ina NON hunting family, and am 100% self taught, I read books and magazines and all I could to learn, but to be honest, I learned more from being outdoors and TRYING, failing and trying again and again, to get good at it
I have hunted all over the place since my early yrs and been very successful, but I spent the time learning, doing and again, even made a lot of mistakes that taught me a lot in the process

keep in mind only about 30% of deer hunters GET a deer, forums and watching TV shows will make you think other wise, but its HUNTING< and NOT shooting!
the only limit in learning how to be a good hunter is YOU< and how much effort you wish to put into it!
more effort,m better you will get!
its how life works
no short cuts really get you much!
enjoy your time out too, don't feel bad if you DON"T get a deer, it should be about fun, not just kills!