I have a switch box that has
1. a white wire that appears to go through from top to bottom;
2. a red wire that come from the top and ends;
3. a red wire that exits at the bottom; and
4. a blue wire that exits at the bottom

I am wiring two switches after replacing one, and the wire came out of their wire nuts so that I have nothing to follow. The switches have only two wires, top right and left (they are timer switches).

How do I wire the switches?

First you need to figure out which is the hot wire ,I think it is the top red.

To test this,touch the top red to the bottom red, a light should go on. Take apart and then touch the top red to the bottom blue, the other light should go on.

If this does not do as I say, then take the other wires and touch together to find out which wire is hot.

If this is the case, take the top red and splice with one wire from each of the timers.

The bottom red splices to one remaining wire on one timer, the blue splices to the remaining wire on the other timer.