There is a clog between the sink and the line to the street or septic tank. The sink is the easier path for the upstairs shower.
the pies are connected so when you turn on the shower the vaulve in the pipe going to the other shower might not be all the way closed thus causing it to leak
The drain is plugged somewhat between the upstairs and downstairs. Need to snake the drains.
Same as upstairs BUT LESS drainage piping BUT more vent piping.
Bad shower valve.
you go upstairs and turn on the shower and chase the cat to the milk
The main drain is plugged. Not completely, but enough that it is easier for the upstairs water to come out in the shower and floor drain instead of going out the drain.
Gravity. Also- If someone takes a shower with the curtain on the outside of the tub this can happen.
You can find a repair guide for the plumbing of a shower on the following site: http://homerepair.about.com/od/plumbingrepair/Plumbing_Repair_DIY_Tips_and_StepByStep_Guides.htm. It is a very helpful resource.
There is a main drain that runs from the basement through the roof where it is the vent for the system. If you look at the layout of the house, the upstairs bath is most likely over the downstairs one or the kitchen. If you look on the roof, you will see a 4 inch pipe coming through the roof that should be over the upstairs bath. The sink and shower drain into that and then to the basement and out of the house. Most likely the main stack is in the wall behind the toilet.
You should let a professional do that, incase there is more damage that you can not see that the water has done.
Do you have an upstairs tenant or the sewer is backing up.