Hi, how do we go from Swissotel Beijing to Birds Nest? Can we swim there or go running at stadium?

You can take the subway line 2 to get to Hepinglibeijie Station from Dongsishitiao Station, which is just under your hotel. Then you can change to line 5 to Huixinxijiebeikou Station and after that you can take a cab to go.
If you go the Birds Nest, you can go skiiing there, but it is not available in other seasons. If you want to swim, you can go to the Water Cube (National Aquatics Center), which is near the Brids Nest.