In december i am going on a mountain trek. how can i build my fitness for it?

Time Crunch: There is not enough time now to "build" your fitness level. If you are currently active, stay with your routine. If not currently exercising, i would not expect too much from the mountain trek as you may not be adequately conditioned. Either way, be smart. Start low and go slow ; go with "one hour / one day" rule; this means that if you're sore one hour later or the next day, you did too much.

Strategy: Find out the elevation, and see if you need to be able to acclimate to the thinner air. Take hikes in similar terrain, learning how to climb inclines while walking. You may find yourself pushing on your thighs/knees with your hands in some places. If you do not have access to this terrain, use incline on treadmill, stairmaster, etc. Learn downhill as well. Find a local hill, repeat ups and downs.