Flash can help to illuminate the room. Think bounced flash. Then, think about how the lights themselves need to be rendered: with a Sloooow shutter speed. Today's small, LED-type lights are pretty low-powered and very,very small, compared to the kind of big 1.25 inch long by 3/4 inch diameter tulip-style Christmas bulbs of the 1960s-1990's...try using the LCD and figuring out how slooooow you can go before the lights start to burn out and look ugly...
If you "really" want to do it up right...you need to use flash + slow shutter speed. Set the camera's white balance to Incandescent, to get the light looking the right color. Then, the flash needs to be brought "down" from 5,500 degrees kelvin to a more orange-ish light that more closely matched the Incandescent white balance, so the flash needs to be fired with an orange full CTO gel taped to it...that will equalize the color temperature of the flash to that of the lights, and will give a very realistic looking Christmas tree and bulbs look.
If one uses JUST the long exposure, the tree doesn't look quite right....if one uses JUST a flash exposure at a fast shutter speed like say 1/200 second, the Christmas tree lights look like teeny tiny specks of light...think along the lines of flash + 1.0 second at f/8 at ISO 400 as a starting point....
If you want to shoot more candid type stuff, like say the gift opening, exposures more like f/2.8 at 1/30 second at ISO 400 to ISO 640 + flash will work nicely.
This is how I'd shoot the gift-opening type stuff...slow speed of 1/30, gelled flash, Incandescent WB, f/2.8.