How to store to lengthen shelf life: a) use a stopper system like Vacuvin (cheap), or b) use nitrogen gas (expensive but works for weeks with most wines, it is used by most wine bars), or c) use a rare gas displacement system (very expensive, circa $10/bottle but the best and worth it for sufficiently expensive wines.

Shelf life: varies with the type of wine, fortified wines such as port, sherry and madeira can last for months without any help, heavy red wines can last a week and even improve, while some white wines last a few hours, less than a day. And then there are the wines where you can't tell

Note that even bad wine is "still good" in the food safety sense ... there is no danger from any pathogens developing. At worst it tastes terrible (I suppose becoming vinegar is the worst case), at best it tastes the same and for some wines actually better.