>> Thinking of going to Lauterbrunnen on 23.12.2018, to watch the waterfall of course but does the fall still happen during winter?
Yes, it should be flowing in December, unless unusually cold weather has frozen it, but it will only be a trickle. It is at its best in spring, when the waterfall is fed by melting snow.
>> Or we should just skip Lauterbrunnen and visit Grindelwald instead?
I would definitely visit both Lauterbrunnen and Grindelwald. The Staubbach Falls is not the only notable thing in the Lauterbrunnen Valley. The whole valley is a magnificent sight, and shouldn't be missed in any season!
If you only had one day in the Jungfrau Region, I would prefer Wengen and/or Mürren over Grindelwald, as I think they are more pleasant for strolling around. If you do the Mürren circuit as suggested in rockoyster's post of May 16, 2018 - 8:53 PM on the following page, you will also experience the beauty of the Lauterbrunnen Valley:
There is a picture with the route marked on this page:
>> How do i get from Grindelwald station to Grindelwald village.
Grindelwald station is right in the village. Just start walking along the main road.
The photo on the following page is looking back to the railway station from the village shopping centre. The railway station is the building with the clocktower in the middle of the photo:
There is a cafe up near the Grindelwald-First gondola valley station where you can eat with great views of the mountains. I haven't been there myself yet, but this is it:
>> Does Grindelwald snow in December? Is it fine to visit Grindelwald during that time?
It sometimes snows there in December. When I was last there, at Christmas in 2016, there was no snow in the village, and very little up at First, but last year they had an early heavy snowfall, and a white Christmas. It is fine to visit in late December, but you will of course need to be warmly dressed.