The bitterness of the KArela varies from pod to pod like CHiles, slice them and sprinkle with salt and let them sit for 15 minutes, then squeeze out the liquid and rinse off the excess Salt. This helps in reducing bitterness to an 'acceptable level
This was a recipe I made with the chinese variety some time ago, Hope it helps..
http://www.panfusine.com/2011/10/thursday-tutorials-call-me-melon.html

Thanks all for the great info about karellas. Can't wait to give them a try

OOPs sorry, forgot to add the link to the Pitlai..
http://dish-a-day-panfusine.blogspot.com/2012/08/day-227-eggplant-pitla-eggplants-in.html

https://www.facebook.com/notes/panfusine/eggplant-pitlai/489015274459873

these are the Indian Variety, you could peel them, slit them vertically to remove the seeds and stuff them with a blend of spices (coriander, cumin, Garam masala, Dried mango chili powder, salt and fennel). then pan fry them until the the surface turns a golden brown..
I like to peel & deseed them, cut them into sticks and pan fry them with potatoes with the same blend of spices sprinkled over>
There is a traditional South Indian stew Called Pitali which is either made with eggplants or Karela.. Here's the recipe for the eggplant variety, but if using the Karela, then simply cut the vegetable in half scoop out the seeds and slice thin (c shaped, no need to remove the spiny surface) and prepare as with the eggplants.

I got it frequently in my CSA box while living in Japan, and my "favorite" way to cook it was with tofu (do a search for goya chanpuru or bitter melon with tofu). Although "favorite" is used quite loosely. It certainly is an acquired taste.

One of our line cooks is a native Thai woman, and when I posed your question to her, she laughed her inimitable laugh while shaking her head and waving her hands in front of her face. I interpret that to reflect AntoniaJames's " acquired taste."

Those are bitter melons. I've never cooked with them, but have had many people tell me that they are an "acquired taste," meaning that if you didn't grow up with them, you probably are not going to enjoy them much. (Every time I ask the people at the Asian farmers' market where I shop what they are and how they use them, they also say, emphatically, things like, "You probably won't like them." I notice that this blog writer is of the same school of thought: http://www.holycowvegan.net/2011/03/stuffed-bitter-melons-karela.html but has an interesting recipe and links to others. Also, you may find more recipes and information is you spell it "karela", or look for "bitter melon" (though the latter may be somewhat over-inclusive as there seem to be several varieties of bitter melon). ;o)