I've been completely honest and clicked "a few manky bits of fruit and veg" although the last such thing we threw away was the end of a cucumber which had gone so soft I put my thumb through it picking it up, that was about two months ago. I'm assuming you are not refering to peelings and such like.
We used to go around the supermarket once a week and buy exactly the same stuff as we did every other week, then throw a fair amount of it away by the end of the week as it had gone furry. Since coming back to Britiain and being on a savings binge for the next trip fund, we have been much more organised and plan a menu every week, then make a list before we go shopping. We get all our fruit and veg from a 'local' farm shop (15 miles away
) and it has a much longer shelf life than supermarket or local greengrocer's produce and is cheaper.
We also keep an eye on things and if (for example) the cauliflower is looking a bit ropey then it's time for cauli cheese, rather than "I fancy chilli, can we have that instead?"
NSTN - there are 2 of us and we used to have a fantastic 3 bay compost heap made of ex pallets which we could easily have enlarged, admittedly that was with a large garden, you should be fine with one of those compost bin thingies.