If it's a repeat flowering rose you need to cut off the flowers as soon as they go over and either lose their petals or turn brown. Cut each one back to a set of leaves coming from the stem. Give it a feed of liquid rose or tomato feed to encourage new flowers.
However, if it is an old fashioned rose or a rambler that flowers just once in a season, dead heading means you will lose any hips that will look decorative in autumn and also feed the birds.
Ask the neighbours if they can remember whether it flowers again. Failing that, dead head half and feed it and see whether you get new flowers or good hips and then you'll know for next year.
Come autumn, give it a good mulch of well rotted manure and/or garden compost and next spring give it some blood, fish and bone or pelleted chicken manure or special rose food to help it make more flowers.