How do you recover an economy? Tear down farms and build cottages? Use specialists? I build courthouses everywhere, I have built Versailles and the Fobidden Palace. I have played around with civics, but I don't understand quite how civics affect the economy. Any help will be greatly appreciated.
Building Cottages is a good idea. Using Specialists is also. Building Research and Wealth are other options, once you reached converter-techs. Building Courthouses is one of the weakest options to recover an economy, because they're very expensive and give only very little benefit, if you don't have like 30+ cities or are ORG. Versaille and the Forbidden Palace are good in games where you pay epic amounts of city maintenance and have a huge spread out empire, normally though, State Property does the job easier and better.
For Civic Economy, your advirsor does show you that! There is the general amount shown, like "none", "low", "high" etc. and on the bottom, you can see, how much maintenance you'll pay for the combination of civis you've chosen. In general, you should choose a civic by the aims you have with your empire, choose HR if you don't have REP, choose Buro if you have a good Capital with OX / WS / HE, choose ORG if you have a well spread Religion and are mainly building Buildings, choose Police-State + Vassalge + Theocracy if building Units, think about running Nationhood when your empire gets very very large and you're in war (the extra Happiness from the Barracks is quite nice then and it's a low-cost-civic), turn on free Religion for maximum Research or for Diplomacy reasons, and never forget to switch to CS + Pacifism once you're in a GA.
Overall, civics don't do too much in maintenance, only if you're very low you should run low-cost civics for their cost, but you can run them nearly always, if there benefits suit you well, because even though they i. e. may give less research on first sight, you get something of that back otoh because you can adjust the science slider higher (due to their lower fee) .
There are articles in the war-academy where you can find the multipliers listed, I think it's *3 for high, but you can do quite well by just looking at the cost listed at the bottom of the advisor, he will give you the absolute amount of money your civcs cost you.
If you have problems with economy-recoverage, get Currency, that actually solves all your problems.