One of my favorite topics . . . and one of the big misconceptions with folks thinking live and fresh cut Christmas trees are like bringing in a can of gas into the home.
First off, don't get wrong. Let one of these trees dry out and yeah . . . they can go up in pretty spectacular fashion. However, a well watered tree can be used safely with just a few precautions.
Pick a tree that is not all dried out. Not all trees are created equal. Depending on where you are some of the trees on the lot may be only cut a day or two before . . . or a few weeks before. The NCTA has several tips on how to select a moist tree -- mostly it has to do with bending the needles and needle drop.
Once the tree is home you should cut off a 1/2 inch or so off the butt to allow the tree to take up water. This is important since these softwoods tend to scab over. You can cut off more, but only a half inch is necessary.
Keeping the tree well hydrated is pretty important. You should check every day . . . maybe even more often if you have pets in the house that think of the Christmas tree stand as a new water dish. Drilling a hole in the center doesn't help . . . ditto for aspirin, baking soda, soda water, fertilizer, commercial additives, etc. Just plain old water is what the tree needs.
When setting up the tree I will say technically you only have to have it meet the clearances to combustibles requirement with the woodstove . . . but as others have mentioned if a pet or youngster accidentally tips over the tree you probably don't want it to land on the stove. In addition, putting it too close to the stove will result in faster drying . . . which is why keeping it well watered is very important.
Of course, only installing UL approved lights, lights that are in good working condition and turning the lights off when leaving the house or going to bed is a good idea.
Here's the video I made a few years back . . . guess I was the best they could come up with as an expert. I don't think this video will launch my Hollywood acting career.
NIST also put out a good video showing the difference between a well watered tree and a dried out tree.