There are a few tricks to making a worn out mattress more comfortable but sometimes these little things can add up to the cost of getting a new mattress set (a cheap one).
One thing people do is place a board underneath the mattress. This does seem to make it feel stiffer as it is basically trying to do the job of worn out box springs.
You can also try to add padding on top of the mattress by using egg crate foam (the low end) to latex or memory foam toppers (the high end). Toppers can be expensive but will give you extra pressure point relief while maybe providing some support depending on how bad your mattress was to begin with.
In the end you would be better off either buying a low end mattress set to see you through until you can get something better or even look into air mattresses. Many blow up mattresses today are better than spring mattresses at the same cost.
You can find a air mattress at Walmart for under a hundred dollars that will do the trick until you can afford something better. Or maybe you will just stick with the air mattress since it is comfy and cheap.