Brinjals are not good for long time storing. So, consume within a few days and store in a cool spot, away from direct sunlight. If not consumed within 2 days, refrigerate by wrapping in a paper towel or perforated plastic bag and use within a week. The inner white flesh turns brown quickly once its cut, so use it as soon as you cut them or refrigerate by placing the remaining on a bowl or plate, but avoid sealing, as it increases decay. 
Brinjals are a prominent part of Indian dry and gravy curries. Also used in lentil soups , stews and rice items. Can be roasted, grilled, baked and stir-fried. Look up the local and popular Vaangibath recipe. 