Get a heavy stand
Growing up, my dad had a traditional stand that looks something like this:
That works for smaller trees as long as you can be sure that nobody (such as a child or pet) will disturb it. That's not at all a given. Remember that trees have extensive root systems that keep them grounded during windy periods and so it's important to get a stand that can simulate the parts of the tree that have been cut off. For that reason, I'm a proponent of a heavier stand such as this one made of cast iron:
There's something to be said for the simplicity of a really heavy, wide stand that will hold your tree firmly in place. I've been told plastic stands are sturdier than they look when they are weighted with water. They have the additional advantage of holding a gallon of water or more, which means you won't risk a dried out tree. In some ways it doesn't matter what the stand looks like since you can always cover it with a tree skirt. (And my wife insists on it even though I like the way our stand looks.)
Placing the tree in the stand
One thing I've tried is to set the tree up before removing the twine that holds the branches in place. This is a mistake for two reasons:
The balance of the tree changes when the branches are fully deployed. A tree that stands straight when wrapped can sometimes end up leaning when unwrapped.
My wife always wants me to rotate the tree so that the best side is facing into the room. Once the tree is secure, you don't want to mess with the balance by trying to move or rotate it.
For the sake of getting a good balance, I also think it's a mistake to attach the stand before putting the tree upright. Or rather, you're going to need to readjust it anyway and it probably won't buy you anything—especially if you have a heavy stand.
Attaching the tree to the stand
Here's where my stand fails me. It attaches to the tree with three screws. Three is the absolute minimum number of points need to hold a trunk in place and it doesn't seem to be enough. If I try to adjust one side, the tree starts falling over and I need help holding it up. (My father's stand had the same problem, but image searches show most of the traditional design have 4 screws plus a ring to hold the truck more securely.)
This year I hit on a solution that's so simple I can't figure out how it didn't occur to me before: I put 2x4 scraps between the screws and the trunk. This has the advantage of spreading the side pressure to a larger area and also makes adjustments easier since the bolts don't screw into the trunk itself. For added security, I packing in extra scraps of wood to brace the tree now that I have it secured to the stand.
Looking around, I see that newer designs use two levels of screws or even "hug" the trunk with a pedal operated cable. I don't have any experience with these designs, but if the stand is heavy enough (see above) they are probably improvements over the three-screw stand that I'm using.
Consider a guyline
Here in California, we are encouraged to secure everything in case of earthquake. Given the excitement of the season, I like to secure our tree in case of childquake. It's a bit of a hassle, but in years past, I've been glad to have a bit of safety from tree fall when its balance shifted due to watering and decorations. It need not be an eyesore either—the line might be secured to a hook in the wall behind the tree.
I've used monofilament fishing line to attach our tree to a hook in the ceiling. Since the fishing line is designed to be invisible (or close to it) in water, most people won't see it. A bonus advantage is that you know what your line is rated and can estimate how many strands will suffice. If you do fish in the summer, its a good idea to replace your line between fishing seasons to avoid tangles, so this is a perfect opportunity.