Once you open a bottle of wine or mead and let oxygen in it will start to oxidise. It should ideally be drunk within a few days of opening however if you are unable to finish and would like to extend the life of the bottle there are some methods you can use to keep it fresher for longer.
Store It In The Fridge
This method is not ideal however it is better than nothing, if you do not have any gadgets this is something you can do to get a little extra time out of your bottle. An actual wine fridge is a better option than a standard kitchen fridge as a kitchen fridge is usually a little too cold for what is ideal.
This is a gas-based system that allows you to purge the air from the top of the bottle with a non-toxic gas (nitrogen, carbon dioxide and argon) that is heavier than air. This creates a barrier to float above and blanket the liquid level to prevent contact with oxygen. These can be bought on eBay or Dan Murphys and will set you back around $30 a can. It can be used 120 around 120 times.
Vacuum pumps are relatively cheap options to extend the bottles life, they work by physically removing some of the air in the top of the bottle. They are typically around $10. Over time they will let air slowly back in so you sometimes need to pump them again every few days.