Looks after itself, really, this shrub, but if yours is old and overgrown hard prune it after its flowering time (should be early spring) and if it doesn't actually produce any flowers, prune it late April/May time. You should find flowering improves the following year - production of fruit is related to flowering and pollination, but also water - if we're not getting much rain throughout the summer, sometimes the fruit either doesn't form, or drops off when its tiny.

Thank you Bamboo. I shall cut it back in the spring.

I have a quince that I do absolutely nothing to and it gives me around a pound of fruit each year.

Now here is a question, is it a tree or a shrub? You see there are two Quince, Chaenomeles japonica which is normally grown as a lowish shrub and Cydonia oblonga (various named froms like Vranja and Queeches Prolific etc.) which is a tree.
A tree has a clear stem whereas a shrub has more than one coming from ground level.
Pruning the tree form is slightly different to pruning the shrub. Read up about pruning pears and follow that advice for a tree type.
Also Cydonia are not as tough as Chaenomeles and if planted in a cold windy area will not thrive.
Sorry to muddy the issue.

Yep, and Cydonia has thorns, whereas chaenomales doesn't

Hi Gertie, I too inherited a quince bush, foolishly I resited it and it died, so please take care :)