As the response below yours points out, you need to have Civil Service to create the chain of farms.
Also, to maintain the fresh water, you have to maintain the chain. You cannot irrigate to the desired squares then cut that chain with a cottage later on, you'll lose the benefits. This is true until you get..ummm...can't remember the name of the tech...the tech that allows you to irrigate non-fresh water squares.
To sum it up...
Pre-Civil Service: you can only irrigate tiles adjacent to fresh water.
Post-Civil Service: you can create chains of irrigated tiles.
Post-Tech XYZ: you can irrigate any square.
edit: typo