At the very beginning of a turn, before you do anything else, click on your faction icon in the lower right hand corner of the control panel, and then open the "Financial" tab on the scroll that pops up. Take a look at where you are financially before you do anything else this turn. The left column will list all your projected income, from farming/taxes/trade/diplomacy and any others, while the right column will list all your projected expenditures for wages/army upkeep/diplomacy as well as recruitment/construction (which you should not have spent any on yet this turn). If the expenditure column is higher than the income column, you're losing money, and you have to see why. The odds are it's your army upkeep, in which case you need to reduce the size of the military.

As mentioned, peasants are the most efficient garrison troop, because they give the most numbers for the cheapest maintenance cost. They can't fight for crap, so don't use them in cities where the garrison has to fight, but you can switch over to peasants in all your rear line cities. Don't have any more garrison than you need, or you're wasting money. You may also have too many troops in the field, so look at that and see if you can do without some of them.

I had similar problems in my early campaigns. I had 5 full 20-unit field armies, and I just wasn't earning enough money to pay that much upkeep. With later campaigns, I learned to keep an eye on those numbers and adjust. Sometimes I get caught without enough troops to deal with a situation that just popped up, but I don't run myself broke through having too many anymore.