I think Eberhart started a really good thread on here about recovering deer. I don't remember disagreeing with him on anything.
As far as me adding value to the thread, my best tips are:
Once you decide to take the animal, from that instant until you pull the trigger, it's just a target. All that should be on your mind is putting a projectile wherever you believe is the magic location. I like the shoulder crease generally because at most angles an arrow that enters there will hit goodies, and it's something easy to see and aim at.
You'll need to mount your weapon or come to draw. Make the necessary movements either very cautiously when the animal is moving or swiftly but smoothly if you cannot see its eyes. Deer have a wide field of vision and if you can see eyeball they can probably see you. If there's a tree trunk between that eyeball and you, congratulations on your temporary invisibility cloak. Use it or loose it. Get as on target as you can as quickly as you can, and stay that way until you loose the projectile.
Once the animal is in range and in position, focus the aim point on that magic spot (crease for me usually) as tightly as possible and focus on nothing but the trigger pull or release. It needs to happen fairly quickly because deer move, but not jerkily.
Once you've shot, the only thing that matters is recovery. I like to have 3 pieces of info available to work with before I climb down:
1. Where the deer was the instant you pulled the trigger. I generally make a quick mental note of this. "OK. Roughly 30 yards out, right to the side of that dead tree." I will circle back mentally and get a compass bearing to the location ONLY after I have the next two pieces of info.
2. Where you lost sight of the deer. If you're lucky, you'll see it fall. If not, you need a compass bearing to the last known location of that deer, and it needs to be as precise as possible.
3. If applicable, a compass bearing to the last place you heard the deer. A lot of times I can hear them running a lot further out than I can maintain visual content. If you're lucky, you'll hear them crash and flop.
If you were watching the deer intently to get this info, chances are you might have picked up on some additional information. Did the deer appear to run smoothly or were they struggling and stumbling and plowing through obstacles as opposed to jumping or swerving? Did you see it bleeding? Was it just a dark spot or streak or could you see blood spraying? Little details like that are helpful, but the most important thing is knowing where they were when you shot and where you lost contact.
Some people are big on trying to watch an arrow. I am not. In low light it can be hard. With a crossbow it can be impossible. And I have found that in my eagerness to try and watch an arrow, I often lose my anchor point or cheek weld and mess up shots. But by all means, if you can get an idea of where you hit, that's invaluable. I generally assume that if I took a shot I felt confident in at a calm deer, I hit close to where I was aiming.
Before you climb down take a minute to text your buddies, your wife, your dad, or whoever you wanna share with. If the deer is in sight keep an eye on it! Dead deer can grow legs. If you can't keep an ear peeled. Drink some water. Munch a granola bar. Calm down before you start descending. Its safer and it gives a well shot deer time to die. Climb down and get your gear together. Take your time.
Quietly go to where you shot the deer. If applicable, search for an arrow. Try and find first blood. This can be fairly difficult. Usually it will just be a spray. If you locate an arrow there are better articles and posts on how to read it. If you can't find the arrow or first blood, walk towards the last known location of the deer while looking for blood. Sometimes they take a while to start bleeding.
If you suspect you gut shot a deer (hunched back, stinky arrow, clear fluids or vegetation/corn/chunky blood) give it as much time as you can stand before you go further. Dead deer ain't gonna get any less dead overnight, but a wounded one can quickly vanish on you if you push him.
On the blood trail, don't just look for blood on the ground. It can show on vegetation and tree trunks too. Deer will often kick up dirt and leaves when they are wounded. Keep a compass in your hand and if possible leave a GPS breadcrumb trail. This can help you tremendously if you lose the trail. Often you will think a deer is running a straight line, but when you glance at the phone or GPS you will notice an obvious curve. Keep an eye out up ahead of you as much as you can, and keep your weapon handy.
If you lose the trail, cannot recover it, and are sure you hit the deer, it's time to "grid search." Hope you have a compass and a GPS. I have only had to grid search one deer. I drew off a 300 yard square on huntstand, and proceeded to move through it like I was plowing a field with about 30-50 yards between the rows. Depending on the situation you may want to make your grid bigger or smaller. You want to cover the terrain in such a way that you are seeing every inch of it. I picked back up on blood about 100 yards away from last know blood and found the deer within 20-30 yards of that.
If a grid search doesn't work, and you cannot get a dog (a luxury i don't personally have access to either) then there's one thing left to do. Give it 48 hours and come back to look for buzzards. I've found one deer this way.
If you still can't find the deer, congratulations. You've gone through an important initiation ritual. Go home, drink a beer, get some rest, and go hunting again as soon as you can. Stuff happens, and anyone who says they've never lost a deer is either lying or hasn't killed many critters. Don't beat yourself up over it. Every predator loses prey, whether it's a house cat or a great white shark. You're not a bad person. If you followed all the above steps, you're not lazy, ignorant, or unskilled. You tried your best and failed. It sucks, but it's not the end of the world.