Keep it growing, feeding regularly, sometimes with a high potash fertiliser to build up the bulb for next year. Toward the end of the summer let it dry out totally but keep it in the pot. Some people turn the pot on its side so no rain gets in - its OK to put it outside in summer.. The leaves will gradually die off. Start to water it again in later winter, or earlier if it starts to grow on its own.

Hi, first of all, we need to establish whether you have actually got an Amaryllis, or a Hippeastrum, so if you could tell us if it's planted with the neck and shoulder of the bulb above the soil, or is it planted with the whole bulb just below soil level, if it's an Amaryllis it will be planted just below soil level, if it's Hippeastrum it will be planted with neck and shoulder above soil level.
The majority of bulbs are wrongly sold as Amaryllis, and are in fact Hippeastrum, which are native to central and south America, Amaryllis is native to South Africa, Derek.

My advice was for Hippeastrum, bearing that in mind.