Find a small container that will hold the wine that is left over to the point were the container is virtually overflowing. Cap the container with a cork or plug so that some of the wine does spill out. (A 375 ml wine bottle works well.)
This way, you will have NO air bubble in the container.
Store the container in your refrigerator. When you are ready to drink it again, remove the container and let it warm-up to the desired drinking temperature, depending on whether it is red or white wine.
You can store your wine this way for about 5 to 7 days. But I would not store it much longer than this.
Another idea for cooks is to freeze leftover wine in ice cube trays, then transfer to air-tight freezer bags to use in sauces. etc.