The proper storage of wine is essential if you are interested in holding on to it for a while.
The first thing to know is that wine should be stored at the proper temperature – keep it cool. Somewhere in the range of 45-65°F. Ideally the wine is kept at a fairly consistent temperature within this range. This is why wine refrigerators are popular. Keeping the wine at a consistent cool temperature will prevent the wine from expanding and contracting with temperature changes. When these fluctuations happen it can cause the corks to leak, or be pushed out. Even if you do see some seepage, or the cork is slightly pushed out the wine may still be fine so try it before coming to a conclusion.
Next you will want to keep it on its side. This is specifically for wines that have a cork. Storing it on its side will keep moisture in contact with the cork and this helps prevent the cork from drying out. A dry cork tends to let in oxygen and will speed up aging and potentially lead to premature spoilage. Screw-capped wines do not need to be stored on their sides, but it will not hurt if you decide to store them this way to save space.
Wines benefit from being stored in dark places. Light can speed up the aging process and can degrade the wine in the bottle.
Humidity can be a good or a bad thing. Try to keep wine bottles somewhere in the realm of 50-80% humidity. Dryer than this can lead to corks drying out and allowing oxygen into the bottle. More humid that this can lead to mold growth on the cork which might not damage the wine itself, but can ruin labels. If you do have a moldy bottle then make sure to clean it off before opening and pouring the wine. Some vodka on a clean paper towel is a good way to remove it from the cork before opening a bottle.
A wine fridge is a good investment if you are storing several expensive bottles of wine. At big box stores you can get a 28 bottle wine fridge for a couple hundred dollars. If you have 10 bottles of wine that you have spent +/- $50 on then a wine fridge like this is a good investment to maintain the integrity of the wine you have spent your hard earned money on.
If you only have a couple bottles then maybe a wine fridge isn’t for you. Just do your best to store your bottles in a cool, dark place, on its side, and don’t plan on waiting more than a year or two to enjoy them.