The best newcomer rule for expansion is the "60%" rule. Once the science slider has been reduced to 60% to cover maintenance for the new cities, stop expanding, and consolidate your position financially.
Cottages are the best way to earn "commerce", but they take time to mature. Once they have matured somewhat, you can continue expanding, either by settler or by force, but its unwise to let your science slider dip below 50%, or you will find yourself in an economic crash.
In a similar way to games like Starcraft, your workers are the meat of your empire. Without them, you wont get far, so building them should be a priority. Most top players start with a worker in their first city, and research a tech that worker can use (if you dont have one already, and often even if you do). For example, if your starting city has Gold on a hill, and you dont start with Mining, then researching Mining while your first worker is building will allow you to "hook up" that resource quicker, likewise if you have Corn in your city cross (affectionately referred to here as your BFC, for Big Fat Cross), Agriculture should be one of your first techs.
Some techs "reveal" other resources, the most important ones are Bronze Working (copper), Animal Husbandry (horses) and Iron Working (iron). Copper and Horses (and iron, for that matter) also allow you to make stronger military units, so their early research should be a priority, especially if your Civ uses one of these resrouces for its Unique Unit. Iron, while still very important, can often be delayed a bit if you have Copper, since you will already have the ability to make a solid military. Exceptions "iron can be delayed a bit" are if your UU uses it (Rome, China) or if you discover no Copper in your area. Iron will allow even stronger units, though, so its still very important.
Since you cannot just make cities willy-nilly, city placement becomes especially important. Choose your locations carefully, with both resources and "military strategy" in mind. Sometimes, you can totally block a neighboring AI Civ off by dropping a city on his "access point" to the rest of the continent. This is especially useful in the long-term, because eventually you WILL have a strong enough economy to expand into the area you have created for yourself.
Hope this helps. Good luck. Prepare to be addicted
