It is commonly called as bitter gourd, other names being bitter melon, bitter apple, bitter squash, balsam-pear.
It is a tropical and subtropical vine of the family Cucurbitaceae, widely grown in Asia, Africa, and the Caribbean for its edible fruit.
It is bitter in taste as you can assume from its name.
It can be used directly in vegetable curries by cutting into pieces. You can find videos in youtube about the cutting process and recipies. You can also deep fry them with a little bit of salt. If you want you can shallow fry it with onions.
However if you want to reduce its bitterness, then you'll have to soak it into lots of salt and keep it aside for an hour or so before cooking.