I've worked my way up from Warlord and just last night completed the 3rd to hardest one (Immortal?). I found my last couple games I end up with copious amounts of gold so here is a couple tips that may be useful. These were all on epic so gold values are probably less on faster game speeds.
* Once you get can trade open borders (writing?), then trade it to all the civs for 50g each rather than a straight swap for open borders. Nice little kick start for the economy.
* If you have plenty of happiness then trading luxury resources for gold is a very good earner, works even better if you can get multiple of the same type as then it doesn't cost you the happiness. Civs tend to pay ~400g.
* Once I get about 1000g I tend to buy a maritime city state as an ally, this allows me to spam trading posts everywhere rather than farms. Costs 750g normally, less if you can destroy a barb camp for them or something first. Basically if its a forest lumber mill, if its a hill mine, otherwise trading post.
* When settling new cities the only thing you should look for is access to new luxury resources, a new city with 2 luxury resources you don't need the happiness from is a free 800g.
* In regards to improvements, never get any +food ones (maritime states is all you need, I end up with 2-3 by mid game). Try and avoid military buildings, unless you have one awesome production city you want to put them in.
* Roads can be a killer early on, if you have cities close together then road them for trade network, if they are a fair distance away (~10 squares is break even I think) then it actually costs you money.
* Avoid more than a couple military units early on, I tend to have my starting warrior and a scout, then pick up a couple archers after my initial worker and monument. Then I hold off for a while, this may not work on deity though, not sure.
* In regards to number of cities I've been going with 4 early on, as long as you can find 4 sites with luxury resources of course.
So my basic plan is pick up gold via trading and barb camps early on and use it to get a maritime city state, that allows me to spam trading posts while still growing. Expansion is done purely to get luxury resources (rivers are of course an added bonus). Try and get 4 good cities up with a minimal military at first, then you can make your plans once you get a solid income and 4 cities at about 8 pop. Pick up second and third maritime states where possible (use their missions as free rep if possible to keep the cost down).
Anyway this might be useful, if not then at least I tried lol.