Fresh Water is a Food item but also a crafting component. To get Fresh Water, you use a Bucket on a Fresh Water pond or lake. The only way to transport and use water is by keeping it in a bucket or watering can. Fresh Water can be stored in Barrels.
Fresh Water is one of the main tile types and can be used to gather Fresh Water with a bucket. It is infinite if not filled in with buckets of other terrain types.
Fresh Water (Deep) is one of the main tile types. At the start of a new map, lakes will be generated. To get more deep water (for fishing, for example), you have to dredge a soil tile with a Crude Dredger next to an existing deep water tile, but deep water is usually surrounded by shallow water. If you attempt to use a bucket to create a land bridge out to deep water, shallow water will automatically spawn around your land bridge preventing you from reaching deep water (see side image). It may be necessary to use mods or cheat mode to produce more deep water.