Hi Firefight - welcome to CivFanatics!
For starters, I don't play multiplayer, so conditions might be a little different. As I understand it, there's a greater propensity for 'always at war' type strategies.
I guess to echo Eastian's comments, at least in Player vs. Machine mode, the two technologies of Code of Laws and Currency are certainly one way of opening the doors for more comfortable expansion: Currency allows you to include

in trades, provides an extra

to all of your cities, and allows the Market building to be constructed. Code of Laws permits Courthouses and the Forbidden Palace, and provides the option of the Caste System where you can run Specialist Artists for getting fat-X border pops quickly so your cities can possibly work more productive tiles, and Specialist Merchants that can deliver a

boost in commerce-poor cities if that's considered advantageous.
"Build cottages!" certainly can help - especially for financial leaders with Cottages on river adjacent tiles get 3

before any Cottage growth.
There are other tactics that you can use:
'Going on the warpath' and razing cities while getting rewarded for capturing cities is one approach, while pillaging enemy tile improvements can add some bonus

.
Working commercial tiles might slow down your growth or productivity, but can provide longer-term advantages.
Settling cities miles away from your capital (high maintenance) or failure to connect cities (share resources and grow) might be a problem area.
Smaller cities cost less to maintain, so using the whip (Slavery civic converts population to hammers) might also cut your costs.
Personally I don't often take the religious path and rely on shrine income to prop up an early-game economy. It requires a concerted effort, and while I'm sure it can be successful as a medium-term and long-term strategy, I am not sure that it's often the best play for the Ancient and Classical Eras from an
economic perspective (diplomatic or citizen contentment perspective is another story).
The actual number of cities that you can support depents a fair amount on the difficulty level, map size, and other variables, so while four cities pre-Currency / pre-CoL isn't a bad 'rule of thumb', it might not be appropriate in all cases.
These are just a few ideas and comments - there are others such as chasing 'commecially' oriented WoWs such as The Great Lighthouse, The Colossus, etc. I'm sure other Civfanatics members will be able to add to this.
