@tbl35 and noting that your skill level will improve with experience
I play on Level 7 (Immortal) usually on small pangaea maps, and as my skill level is still improving, I've easily beaten the AI's in my last few games (OK I lost my first couple games on Lv 7 maybe 6 weeks ago when I stepped up from Lv6). What EasyGoin says here basically hits the nail squarely on the head, except than on Immortal, unless no AI is at all strong, you'll be beaten to Chichen and often to Machu and for that matter usually to Taj. (On level 6, you can usually get some(most) of those wonders if developing well)
The one wonder that I can usually get on Immortal, Forbidden Palace, is getting somewhat of a nerf in the patch (that seeks to KILL anything that resembles ICS). (I also can, if desired, easily beat the AI's to Stonehedge, which for the price of two monuments provides 4 times the culture, costs no upkeep and gives me GE points.
I don't want this to be too long a post, but I play like a Borg (StarTrek) Puppet Master and basically puppet almost everything and only raze poor cities in poor spots that don't fit my planned road network and don't have happiness buildings or wonders.
I, rather quickly connect new found and conquered cities to my road network and this helps trade income as these cities grow. Meritocracy keeps my happiness in check (although getting nerfed so I may have to raze more post patch). By not founding too many of my own cities early on, I keep cultural costs down and am not severelu unhappy. That being said, founding 4 or 5 new cities and then once they hit pop 3 or 4 putting them all on production focus and cranking out an army and attacking is quite strong.
Once you have a decent puppet empire, used some workers (preferably captured) to replace some of your puppets' farms with TPs. This will give you more gold since they run Gold Focus, and also somewhat slow down their growth if happiness is an issue. Once you get the SP from the Rationism Tree that give you 1 science per TP, your tech level jumps as well and the TP spam becomes awesome.
My maps around turn 250 (assuming they go that long as they usually do) have TPs all over my puppets' land. Most of my founded cities (or any that I rarely annex) are more production oriented and have mines on hills rather than TPs (although I may switch some mines to TPs if I feel the need). I also may build a few early river farms and switch them to TPs.
By attacking someone early and often, I can usually take a few cities, get more space for my empire, cripple an nearby future enemy, and have a few workers to use as slave labor. My money is used to by military and to bribe CS and for some RA's. Very rarely do I buy a settler or worker. I'll buy a settler if it is absolutely imperative to make a city to stem AI expansion that may break my trade route or if I much simply have a luxury (settle right on it). I'll basically only buy a worker if I absolutely must improve a luxury asap to prevent crippling unhappiness.
So, in summary and noting Emperor is easier than Immortal. Make an army and go out and take a few AI cities and put TPs in them and connect them to your trade route.
Captured workers can often do all this for you. I often am building roads towards the front, both to speed reinforcements and to mean that my newly conquered cities are connected to my trade routes quicker. AI cities tend to quickly be decent size on Immortal and often there's a quick jump in income once connected.
.. neilkaz ..