The main concerns to storing your wine are:
Wine is best stored between 40-65°F (4-18°C), optimally between 55-57°F (13-14°C). Even more important is temperature stability. Optimally the temperature in the cellar shouldn't fluctuate more than 5°F (2-3°c) in a year. This keeps oxygen from being drawn into the bottle, upsetting the freshness or even spoiling the wine. Maintaining this sort of stability can be hard to achieve, so simply do the best you can. A Refrigerator/Freezer Thermometer will help you determine the temperature of your refrigerator.
Also, keep the wine at a humidity above 50% and below 80% as this is enough to keep your cork from breaking down but dry enough to keep mildew from growing on the cork or label.
It's a good idea to keep the storage area somewhat ventilated and odor-free. Air will inevitably pass into your wine so the odorous matter in the air will make its way into your wine.
Finally, wine should be kept out of sunlight. as the light waves can breakdown the more complex particles in your wine. Packaging your wine in dark bottles (green or brown, find our wine bottles for sale here) will also help absorb harmful light.