Here are a few tips I've picked up over the years to keep food fresh.
Lettuce - never use a metal knife to slice a lettuce. The metal will turn the remaining lettuce brown and make it less appealing. Instead tear it with your hands or use a plastic knife.Pasta and rice - keep your dry goods fresh and free from insects by storing them in a glass jar with a lid along with a bay leaf
Sliced fruit - keep sliced fruit like apples and fruit salad looking fresh by storing them in the fridge in water and lemon juice.
Cheese - wrap cheese tightly and keep in the fridge. If mold does appear it will normally only be the edges, which can be easily sliced off. If a block of cheese dries out, store it in the freezer and use it grated in your recipes (it does not need to be thawed).
Screw Tops - Always buy screw top bottles and save them to store your homemade goods in. They are also great for storing dehydrated foods.
Leftovers - never throw anything out, most leftovers can be added to something else to make a completely separate meal or frozen for later use.
A few frugal suggestions for using leftovers are:
Cooked vegetables - can be used in soups, pies, or as potato toppings
Stale bread - bread pudding, toasted and used as croutons on soup.
Left over meat or fish - used as ingredients for a chilli, added to fried rice or stews.