How are layers of sediment laid down in water?

In water systems, sediment is the unconsolidated mineral matter carried by wind, water, or ice. In some settings, organic material may also be considered to be sediment. Mineral sediments are mostly a result of erosional processes - in a river. For instance, the water will carve material away from the river bank and river bed and transport it downstream. Other material is blown into the river, adding to the sedimentary load. On the other hand, organic material is often the result of the decay of dead organisms. Algae, for instance, will die and add to the sediment load. 

Using a river as an example, consider material deposited upstream. As the river flows, it will carry this material downstream. Along the way, some of the material will remain suspended in the water - if it's light enough, the river can continue to carry it. Other materials are carried and dropped before reaching a terminal location downstream. The stream capacity is the factor that determines how much of a sediment is transported and where it will be dropped. As a stream picks up sediment, the total load of material gets heavier. Although the river may be able to sustain the load for some time, it will eventually become too heavy to move. At some point, enough material will be added to the load to overwhelm the river and the river will leave some material behind.

Over time, the deposited sediments will build onto the river bed in layers. Since the eroded and deposited material will differ over time with seasonal changes, wind changes, and material changes, the sediment layers will be identifiably different. For more information on sedimentary processes, check out the included link.