Every improvement you make has a certain gold upkeep cost, and if you want to play well, you need to keep it in mind before you build it. Look at
this chart, or the civilopedia in-game to see if a structure is worth the upkeep.
For example, if you have a library, it will cost you 1 gold, or to think of it another way, one trade. If your city made 2 light bulbs before the library, it will make 3 after, which is a difference of 1 trade. To make the library useful, it needs to make at least 2 extra light bulbs to offset the upkeep and make a profit, which means you need to make at least 4 light bulbs without the library.
For temple, colosseum, and cathedral, you can think of each person made content as 2 trade, since you could also satisfy a citizen by making 2 luxuries. Do the math, and a temple is worth (in ideal conditions) 3 trade, a colosseum 2 trade, and a cathedral 5 trade. The colosseum barely pays for itself in ideal conditions, and should almost never be built.
I almost never build granary and barracks. Granary is useless once you're in Republic/Democracy and can celebrate
WLTPD, and really isn't that great even before that. Barracks is only good if you're pumping out units like mad, and it does nothing for you when you're building anything but a military unit.
Anyway, that's how you save money. To make money, you can hit huts and hope for 50 gold; you can let a barbarian attack you, hope it loses, and position a unit behind to take the leader and collect ransom; you can demand tribute from a small nation that's afraid of you; you can capture a city and take the spoils; you can take a caravan to a distant foreign city for a trade bonus; or you can collect taxes.
Usually most of your money comes from taxes. Besides raising your tax rate, you can increase trade by switching your workers to ocean/gems/gold/river, and building roads on plains/grassland/desert. Also be sure to open trade routes with your biggest trade cities. If you're already making some money, marketplace and then bank may be worth it. And switch to Republic/Democracy, please.
Despotism has its uses, but from what you said, it's clear you're using it wrong. Despotism is best for huge early military campaigns, like if you're clearing some space to grow in or trying to conquer the world. In Despotism, most city improvements won't be worth it because you're making so little trade and growing so slow. Temple/colosseum/cathedral aren't useful because you can make people content by martial law, and marketplace/library etc. aren't useful because you don't have enough trade to multiply by 1.5. In despotism, you should be making units, MAYBE barracks. Granary is a waste of time in which you could be building units. Otherwise, you should switch governments.
