The best thing to do is to keep them in their pots and keep them watered having cut off the flower spikes. Once the weather improves they can be planted outside where they will flower year after year. Do not, on any account, cut off the leaves as they produce the goodness to enable the bulb to flower next year.
This is what I do. Cut off all leaves, chuck the leaves, soil and moss in the compost container, let the bulbs dry in a cool place NOT in plastic containers, but in old shoeboxes. In the autumn plant them in the garden. In flowerbeds, or in big tubs, ten or so at a time. They will flower again. I am looking out of my window as I type, and I see last year's potted hyacinths are now in my big pots, just breaking into bloom. They come back year after year.