Hi there!
Im new to civ 4, but a HUGE civ 3 person. I noticed something. When would you want to build a cottage compared to an irrigation. I can't tell the difference.
A farm will increase the food production of a tile by +1; a cottage will increase its commerce production by +1.
The food production of the farm will not increase until Biology boosts it by 1, and not ever again after that.
The cottage, however, provided you have a citizen working that tile steadily, will gradually increase its commerce production from +1 (cottage), to +2 (hamlet), +3 (village), and then +4 (town). In turn, these values will be increased by researching the Printing Press technology (+1 commerce from villages and towns) and by running the Free Speech civic (+2 commerce from towns). Commerce allows you to keep the science slider raised nice and high, and what doesn't go to science gets converted to gold, which lets you buy all sorts of nifty things.
Oh, and a leader with the Financial trait gets a +1 commerce boost on these cottage tiles as soon as they yield 2 commerce.
So cottages are better, right? No, not always. You'll inevitably need some farms to help the city grow, and to ensure your citizens can either work low-food but high-production tiles like mined hills, or to convert citizens into specialists.
Ideally it's best to have your cities specialize--some should try to have as many cottages as possible and become commerce engines, while others will have many, many farms and run specialists to produce great people, which still others will have a mix of farms, mines, watermills, and workshops in order to become production powerhouses.
I myself prefer to have a city with a lot of river tiles specialize as cottage-heavy commerce cities. My reasons are, first, a riverside tile already produces 1 commerce, so it will boost a cottage throughout the game. Second, riverside grasslands produce 2 food, sufficient to feed the citizen working that tile, while flood plains with a cottage produce 3 food, which feeds the citizen and fuels growth. (Riverside plains tiles usually get farms.) And again, for a Financial leader, a cottage beside a river instantly goes from +1 commerce to +3.