You can collect potable water from rivers and lakes. All you need is Bamboo Cup or a Bucket.
In this example we used a bucket, equipping it on the Hand button. Then tap the water and wait for the Filled bucket icon to appear on the upper left.
To transfer the water to your inventory (backpack button) just tap the green button with the filled bucket in it. It will open the container dialog and you can drag each water to the inventory.
Also, you can always find water on Water Springs and Cactus. Remember to drink some water eventually to recover your stamina (indicated by the blue bar on the grey character button). Low Stamina levels will make you weak and slow.