It's a little hard to tell, because I don't know if maybe there's something specific you're missing or if maybe it's just an overall efficiency problem.
Obviously, you'll need to get commerce from somewhere. Usually this will be through cottages or, if the food situation permits, farms with aristocracy. It helps if you can determine one or two dedicated commerce cities with a river and maybe some high-commerce resources and have them focus on multiplier buildings.
Alternatively, you can focus on farms to get some high-food cities and use specialists. This means you might actually have a fairly low setting on the research slider (e.g. to take advantage of gambling houses), but still get the research you need from scientists. I've never played a specialist economy in FfH, so I can't tell you much about the specifics, such as which techs make good lightbulbing targets etc.
Either way, you'll need enough workers. You're playing on Emperor, so I suppose I don't really need to tell you this. When you settle a new city, a worker should be in the area and start building improvements right away.
Trade routes can be hugely important. I had a game recently where I had swallowed up my neighbor and was barely holding on to my eco at 0-10% research with 10ish cities (one trade route each). After acquiring the techs to open two more trade routes shortly after, I was sitting comfortably at 40%, even though in those few turns, my tile-based eco hardly changed. Try to get open borders with anyone you can, use a hawk or two to expore and contact faraway civs. Overseas contacts are especially valuable if you can trade with them (i.e. there's a coastal connection).
Make sure you're running the right civics. Once you grow beyond a handful of cities, God King will become very expensive in terms of maintenance, while the gains don't make a big difference for your whole empire any more. Switch to Aristocracy if you have the food (with Agriculturianism and/or Sanitation researched), City States otherwise. You may find that after expansion, your capital is not very central any more, building the Summer Palace or relocating the palace can help save a lot of maintenance cost.
Buildings help, but don't overdo it. I tend to build markets and elder councils everywhere unless there's something urgent to build like a worker/settler/military unit. Build multiplier buildings in high-commerce cities, build units elsewhere instead. Skip those multipliers in low-commerce cities; 25% of 5ish beakers isn't worth the hammers for a library. Same for courthouses; if your city maintenance is less that around 10, often a multiplier building will give you better returns for your hammer investment.
