Just in contrast, my own approach is almost the complete opposite of Stylesrj's.

Riverside tiles, especially flood plains and grasslands, get cottages. Why? By being next to a river, they earn +1 commerce, which adds up. Since they produce 3 and 2 food (respectively), flood plains and grasslands will feed the citizen working them. Plains get farms, but are rarely worked until late in the game.
Why? It's all about food, and plains have very low food output. Yes, they provide 1 hammer, but I can mine a hill and get 3 or 4 hammers from it, and 1 food if it's a grassland hill; or work a forest and get food and more hammers than plains. Until you discover Biology and increase their food output by 1, plains tiles aren't much to write home about.
At any rate, as Stylesrj said, much depends on city placement, and city placement in turn determines specialization. I will place a city amidst a plethora of flood plains and grassland river tiles to make it a top-notch commerce/science city. I cottage tiles as much as I can in that case. A city with some good food resources and good production tiles, however, gets very few cottages, if any. It's a production centre, for military units and other expensive builds, possibly including wonders.
As for specialists--you need extra food. I can't emphasize that enough. So some tiles that I might normally cottage may get farms. Many people are fond of designating one food-rich city as their "Great Person Farm" (GP Farm). They'll improve all its tiles with whatever will maximize food production (farms, windmills on hills instead of mines). This allows them to run as many specialists as possible, which increases Great Person production.
I myself am fond of the science super-city approach. A city with a good blend of production, cottageable tiles (again, rivers), and food will get this designation. It's usually the capital, as they tend to be in excellent spots, and will additionally benefit from the commerce and production boost from Bureaucracy. I want this city to produce most of my Great People, most of whom should and will be Great Scientists who in my opinion are the most useful and desirable of the Great People--well, except Great Engineers, but they're harder to get.
So building a library in this city is an early priority, as it allows me to run scientists early on. I'll also try to build the Great Library here for its 2 free scientists. Later, I'll add whatever monasteries I can, a university, an observatory, Oxford University, and a Laboratory--all to max out its science production. I'll use one of the first Great Scientists to build an Academy in this city, then I'll "merge" subsequent one with the city to increase its science output. (Though I may use one or two GS to "lightbulb" key technologies--I'm fond of using my first Great Scientist to discover Philosophy, for example.) I'll mostly cottage the super science city's surrounding tiles, especially tiles next to a river, but later in the game when I can run more scientists thanks to its buildings I may turn to farming instead.
Keep in mind most of what I just said applies to a cottage economy. If you go the specialist economy route, everything changes. There are many threads here dealing with the SE, but if you're still feeling new to Civ, I'd get the cottage economy basics down first--it works great at Monarch level and lower.