I'm in shock but it's not your fault if you've not been set an example. Good for you for asking and trying to do something about it.
We had a chicken the other weekend and it did us, in various forms, about 15 meals.
4x roast chicken meals (2 adults, 2 children)
6x chicken and leek pie meals (about 2 adults, 4 children)
6x lentil soup meals (mainly adult)
After taking what you want for your roast dinner, strip off as much meat as you can - any knuckles or other chewy bits that you don't want put aside with the carcass (and you want to keep all the carcass, skin, bone, gristle, as it's full of nutrients and things like collagen). Don't forget the beautiful 'oysters' underneath the carcass - two little dells of bone either side of the spine that are filled with the most tender and delicious circles of meat - no need to cut; just feel for them and pull away with your fingers.
Chop leek and dice carrots - or any kind of 'pie' veg that you fancy really - fry in butter for a bit and then use that butter to make a white sauce 'around' them (40g butter, 40g flour, 1 pint whole milk). Season and add one or two decent spoons of wholegrain mustard. Chunk up the chicken and add to the sauce, then put in a dish. Make and roll out quick flaky pastry or use a pre-rolled puff pastry sheet and lay it over the top. If you have offcuts of pastry make some leaves and flowers (just roll up strips of pastry) and arrange decoratively on top, and then egg-wash. Bake at about 170degs (fan) for about 30-40 mins.
To make chicken stock with the carcass for soup, try to chop up the bones a bit. I usually leave the wings alone and pick the meat off after making the stock, as they are fiddly. Cut 1-2 carrots in rounds, and chop 2 celery sticks into pieces. Roughly cut up an onion and a few cloves of garlic. In a large pan, fry the veg gently in oil and then add the chicken bones and brown off - this develops flavour. Add a load of salt - about 2-3 tsps? - herbs, pepper or peppercorns (4) and 1-2 bay leaves, and cover in about 1 litre of water. Bring to the boil, then cover and leave it to simmer for at least an hour. Drain using a sieve (obviously, retain the stock) and then use to make soup. I pick off any good bits of meat that have become accessible and drop them into the stock. This is the point where you throw away your chicken! I don't keep these veg usually, as they've been boiled a lot, but some people do. I made this lentil soup the other day and it was lush.
I know it seems like a fag but really it isn't if you have a few staples in your house, and then obviously your chicken goes a lot further. Celery, carrots and onions are not expensive, and when you consider a nice pie will usually cost about £3 for one portion, it's good value.