Once a bottle is opened, most wine has a very limited life. All but very mature wine will improve for a while when exposed to the air, but over time all wine will oxidise and become unpalatable.
The best thing to do with a bottle of wine is to drink it all at one sitting. If you fail to do that, then there are several options for preserving it in good condition for a few days.
Chilling any wine, including reds, will help to preserve them. All reaction rates, including oxidation by air, will decrease at low temperatures.
These pump air out of the bottle. The less air there is, the less oxygen is around to spoil the wine. The problem with hand-held systems is that you are likely to remove some of the desirable chemicals as well. Commercial systems claim to pump the air out more precisely, without affecting the volatile compounds in the wine.
Inert gas systems – hand-held
The gas cannister dispenses an inert gas on top of the wine; this is heavier than air and displaces it. Pouring wine from a bottle will agitate what is left in the bottle, and dissolve some more air into the wine. The inert gas will not keep the wine for prolonged periods, but it works well for several days.
Inert gas systems – commercial
These use an inert gas to force wine out of the bottle, and through a nozzle into a glass. No extra air is introduced into the bottle. Enomatic is the market leader, and their website provides more details. These systems allow restaurants, wine bars, and shops to sell wine by the glass, even if it takes weeks to empty the bottle.
Plastic film on top of the wine
A company called Wine Shield sells specially designed thin plastic film, which sits on top of the wine in a bottle. This aims to keep air away from the wine. I haven’t tried it, but it does sound plausible.
A simple and reliable approach
I pour wine into a smaller bottle, and fill it. Pour with care so as not to introduce too much air. Then stopper it and put it in the fridge. Depending on the wine, this is fine for a couple of days. It lasts longer if you squirt some inert gas above the wine.