DO NOT fill the snow globe with plain tap water. Depending on your area, minerals can cause the water to become cloudy. Use distilled water instead. Also, depending on the size of the globe add glycerin to increase the buoyancy of the snow. Without it, the flakes will fall quickly to the base. For example a 3" globe will need 8-10 drops.
The base usually comes off quite easily if you place it in a container of warm (from your faucet) water. Chang the water frequently to soften the glue. You'll find a rubber plug which can be reused. Make sure you place a dab of silicone glue on the plug before inserting to prevent leakage.
George Maxwell, January 2009