Someone touched on my biggest tip.
REMOVE your rifle sling. Physically remove it. Put it in your pocket or pack. Put it on when you're dragging him out. Quick detach sling swivels.
If the sling isn't on the rifle, you're less likely to get lazy and get caught with a rifle on your shoulder.
A still hunting or tracking gun should be a weapon for the purpose. I'm not toting a 26" barrel and 12 or 14 or 18x scoped rifle.
I have 2 rifles setup for still hunting/tracking. A slightly modified Kimber Montana with a 2.5-8x36 VXiii for nice weather.l..weighs like 5.8 pounds scoped..and a 7600 35 whelen carbine I put a straight combed wood stock on. It has a Williams WGRS receiver sight with no apeture. A lot of days, a scope isn't a smart idea. Rain, snow, fog...raise the rifle and exhale and it's game over...my rigs are light, compact, fast handling and quick to shoulder and on target.
I don't care what those rifles do off a bench at 100 or 200 yards. I care that I can comfortably carry them all day on my feet and they come up to my eye naturally.
Not saying you gotta go out and buy a new rig...but, if you fall in love with tracking and still hunting, you'll see what I mean. My rifle is in my hands ALL day. I carried Remington pumps sight the same 2.5-8x36s for a while but man, they are heavy. I am about in love with the Kimber and excited to carry it this season.
Learning deer bedding is my other go-to. There's only so many hours in a day. There's only so many days in a season...and unfortunately I have to work. I don't have time to waste. I don't waste my time inching along through places I don't expect to find my target. And I focus my efforts where I DO expect to find my target. If that's doe hunting, it can be different than if I'm after a mature buck. Do I spook some deer? Absolutely... but typically not what I'm looking for. Not likely to find a mature buck waltzing around a mature oak flat a couple hundred yards from a parking area at noon within a few days of the opener. So I blow through areas like that fairly quick. I will be careful and not make a ton of noise...but also not inching through.
Binoculars are huge for me. I am learning to use them more and more. Again, back to time, I don't spend as much time glassing as some guys will. Do I miss some deer? Yep sometimes.
Learning your deer and land is huge. But I often use still hunting to learn new areas and scout. I carry my GPS and OnX on my phone and I'm constantly marking stuff for the future.
If you jump a deer don't freak out. You know he's there. You know the direction he ran. If you are sneaking along, chances are he's not going too terribly far. Go find him and kill him! I give them a bit to cool down...look at the land, look at my maps...devise a plan and go hunt him down. I've had mature bucks not go 200yds and bed back down after I've nearly stepped on them. Or, once they are jumped, often times they decide "I'm on my feet...I might as well grab a snack".
You can't overthink the wind. Keeping it in your face is great....but not always possible. I often hunt a cross wind. If it's blowing from my right side, I know I don't have to focus immediately to my left. Again, time...don't waste time looking where deer simply aren't gunna be.
On that note, TURN AROUND once in a while! Just because you walked through there doesn't mean a deer didn't come up or down the hill or whatever since then. One of the first coyotes I've ever killed was on a bear drive. I was pushing down along a small creek bottom. For no reason, I turned around to catch a coyote sneaking off the hill from another driver and cross the creek. I put him in a pile.
As the day changes so does my hunting. If I'm after a mature buck I focus primarily on bedding locations outside morning and evening. Then I will spend more time in areas coming from bedding to feeding.
Also gotta remember once the pressure drops, deer go back to being deer and the rut isn't over. Can't tell you how many bucks I've gotten the drop on because he was busy being a buck and chasing does. Couple years back we just finished pushing a woodlot. The crew was done. I had a buck tag and an hour of daylight on the last day. I still hunted through a really thick area...low and behold a buck...chasing doe around like a madman. He wasn't something I wanted to shoot so I enjoyed the show.
To me, it's a very enjoyable way to hunt. Im not sitting there hoping a deer comes by. I'm going to find them. I cover a lot of prime ground. I get to scout and log stuff for the future. I can also cross stuff off the list. If I am hunting an area a couple days in a row, there's areas I won't bother going back to...other areas may have been promising and I will re-hunt them.
Rather have snow so I can track...but that's rare...
Oh...on that note ... conditions. There's days I simply won't bother still hunting or tracking. Those dead calm days where you can hear a mouse 200 yards away? Ya...I'm not gunna bother. I simply don't have the patience to move that slowly and quietly to get away with it. Give me rain or wind or wet ground or soft snow....heavily frozen leaves and zero wind...no thanx lol. But, I've learned to adapt some. There's places I know I can hunt on those days. Pines and hemlock areas can be great on those days as well as some others....think outside the box. Take advantage of everything can.
There's a learning curve. It's not difficult but it's not easy for most people. For me, it was frustrating as heck for a while because I like to move and cover ground. I still do. But I'm learning more and more when to hunt and when to cover ground.