Let me throw my 2 cents in and try to clarify the earlier post:
You CANT irrigate by Sea or Ocean or Coast water squares, until you develop electricity (then you do some business with salt water ionization or whatever).
Before electricity, you can ONLY irrigate FLAT land (no hills like older civs) that is ADJACENT to a stream and/or FRESH water lake.
How do you know a lake is FRESH water? If its inside land you know.
The ideal city is one that has a stream going through its usable squares.... not just for irrigation, but for hydro plants later on... no stream (aka river) - no hydro. ALSO you get a 'free' aquaduct when on freshwater.
Streams tend to mean good city spots in general.
Now say you got a stream surrounded by nice grassland, but about 9 tiles away is a very plains/desert spot that you want to build a city on... EASY.... you can chain-irrigate towards the spot you want.
That irrigation does NOT count for freshwater for the city improves mentioned above... but it sure can help out a desert area alot... I have had mainly plains citys well into the teens when irrigated well - and good production rates too.
Hope that helps.