The simplest way to keep wine fresh is to insert the cork back into the bottle right away and place the bottle in the refrigerator. Refrigeration is the best way to slow down oxidation once a wine is opened and exposed to the air.
There are numerous devices on the market used to preserve wine. There are small hand pumps used to draw oxygen out of the bottle and a small can that will put nitrogen back into the bottle. Both devices limit oxygen exposure in the wine but can be tricky to use and of course, cost money.
I personally think using the original cork is the best way to preserve your leftover wine. Pop in the cork back right away, stick the bottle in the refrigerator, and enjoy the next day.
For more information, you might want to Google "how to keep open wine fresh". You could find a few more ways to keep your open wine fresh.