There are many oases in the Tarim Basin of the Takla Makan desert. The melting snows from the surrounding mountains flow down into the sand, and at the lowest point in the desert, that is where the water emerges.
The Mountains
There are many mountains surrounding the Takla Makan desert, like the Kunlun and the Pamir mountains. You can go hiking, and see the amount of snow that sits on top of the mountains. I would recommend taking a guide with you, as you don't know what kinds of trouble you will encounter there.