Before you do anything, read up on the regulations for tree stands in your area. There may be certain locations that are off limits. If you plan to hunt on someone's private property, clear the location with the owner before you do anything else.
The next step to picking a tree stand location is finding a place where you'll find game. When hunting deer, this is called looking for deer sign. Deer sign includes scat (deer feces), deer tracks, shed antlers and scars along tree trunks where deer have rubbed their antlers against the bark. You can also look for signs of feeding -- are the plants in the area clipped short? That's a good sign that deer have been using the area to feed.
Once you've found an area that has a lot of game traffic, it's time to look for a good tree. You need a strong, live tree. Avoid trees that have lots of dead limbs or other signs of disease or decay. Try to find a tree that has bark with a semi-rough texture. Tree stands don't work well with trees that have smooth or flaky bark. If you're using a climbing stand, you'll need a straight tree that doesn't have a lot of branches low to the ground or you won't be able to climb up. You can clear some branches away using shears or a small handsaw.
When you've chosen the tree, you need to decide which direction you'll be facing when you're hunting. Pick a direction that faces most of the deer sign. Try to avoid a position that has limited visibility -- you want as much flexibility as you can manage. If you're planning on hunting the same day that you're setting up your stand, you'll want to be upwind of the deer (or other game) if possible. You don't want your target to detect your scent and run off. Tree stands help mask your scent, but taking the wind's direction into account can also help.
You may need to clear some brush out of the way to give yourself some shooting lanes with clear lines of sight. Try to pick a position that gives you multiple shooting lanes. This will give you more options when you have an opportunity to make a kill.
Some hunters prefer to set up a stand several days in advance of a hunt. That way, the deer have a chance to become accustomed to the gear the hunter leaves behind. As an added benefit, the hunter won't have to carry as much equipment on the next visit. It's also a good idea to try to mask your scent as much as you can -- otherwise you may frighten off your quarry.