How to keep fruits and vegetables fresh

As for fruits (including, for example, tomatoes), ethylene gas is released by fruits and causes them to ripen. You can buy "produce bags" that absorb ethylene gas, and slow the process of ripening. (Some fridges have drawers that absorb ethylene gas, but I doubt you feel like buying a new fridge.)

Update: See Vicky's answer and my comment for a couple links to examples of the "produce bags." In addition to removing the ethylene, the bags claim to also work by "breathing" and "reducing moisture formation."

For vegetables, it sort of depends. If you have root vegetables like carrots and beets, put them in water in the fridge (with the stems cut off), changing the water regularly. The roots will absorb the water (as they do in the ground) and thus stay quite turgid.

If you're in the UK Lakeland sell Stayfresh Longer bags: http://www.lakeland.co.uk/stayfresh-longer-bags/F/keyword/vegtable+bags/product/1932_1094_1092 which really work extremely well. I'm sure there are similar products available elsewhere.

I have no idea how they work, though!

Normally, all sorts of vegetable remain fresh for a longer period if you keep them in large earthen wares.chiilies, capsicum and some leafy veg when kept in glass jars with lid on remain fresh for 10 to 15 days. You must see to it that these are properly wiped to remove water particles before storing them the way I suggested.