lifted from the FAQ
"I`m in debt what do I do?
if you are in Debt, first disband all ships. Then, stop using turns. After doing these steps, sell minerals/goods/food/ore/etc on the Market. You can check your "Income" screen to see if you will make money if you use turns. Sometimes you can dig out of debt just by using turns, although if you are in bad debt it is suggested you don`t try this way. If nothing else, you can restart your Empire."
Hi =)
When you are in debt, there will be a debt interest for every turn you spent. Therefore you will be deeper in debt each time to use a turn.
However if for example, you get into debt due to the upkeep of your fleet. You then immediately disband your fleet. Your income now might be more then the debt you are facing especially if you are an establish empire
You might be able to get out of debt in this manner =). However it is thoroughly advise to keep a small stock of minerals in the market for emergencies like this. Selling resources to get out of debt is the most common way to get out of it.
Have fun