Welcome to CFC, Broletariat!
There are a variety of things that can cause the problems you describe:
1) Not enough roads. Every time to you add a road to a tile, it adds +1 commerce to the tile. A citizen will have to work the tile to collect it.
2) Building everything, just because you can. Every building costs maintenance. Build the stuff you need to win, but don't build stuff you don't need. The Golden Rule of Improvements: A city needs nothing to survive. The question is what the empire needs for the city to have.
3) Learn how to use the lux and science sliders. If you haven't found them, hit F1. They're at the top of the screen and control the imperial budget.
4) Failing to have enough workers. Remember the roads I mentioned? You'll need lots of workers if you're going to road every tile. Shoot for 2 workers per city. Don't hesitate to buy them from the AI, if they become available, or to poach a settler pair here and there.
5) Putting a garrison in cities while in Republic. Monetarily, Republic is often the way to go. It adds +1 commerce to every tile already producing at least one. So: Non-riverside grass = 0 commerce. Add a road, it becomes 1 commerce. Switch to Republic, it becomes 2 commerce. However, Republic has no MP effect. So if you leave tons of spears sitting in cities safe from attack, that's all those spears do: sit. Oh, and cost upkeep if you're over the troop limit.
Really, the best advice I can give you is to post a save. It's much easier to tell exactly where the problem is if we can take a look at your game.