Depends on how long you intend to store them. For long term storage, ie, longer than 3 months, I'd recommend a good wine fridge which maintains temp and humidity for optimum aging of wines.
For short term, you can just put them in a carton horizontally, and put the carton under your bed. Basically find a place in the house where the temperature is not excessively warm, or varies too much during the day.
Uncorked, unfinished white wines can be corked back and placed in the fridge. White wines can last for weeks on end this way. Some supermarket white wines come in screw caps which make it very convenient for recapping.
Uncorked and unfinished red wines are a bit more troublesome. If you simply cork it back and place it in the fridge, it may still taste good after 3 days, but beyond that, good luck to you. To preserve wines beyond 3 days after opening, you can either get a vacuum valve and pump out the air from the bottle prior to putting it in the fridge, or use an inert gas product that you can spray into the bottle prior to re-corking. These methods can preserve wines up to a week or more.
Ice wines can be kept with the above methods, but because it is so sweet, it tends to be more resilient and does not deteriorate that quickly.