I made an impulse buy in the grocery store today and bought some black-tip shark and albacore tuna steaks. The Tuna was awesome but the shark made me want to throw up. What is the best way to cook it? I prefer using the stove as I have no grill at the moment.

Need to soak in milk for a couple hours and the grill..... Thats the only way I have had it. Maybe sear it in a pan. I threw some garlic salt and a little pepper on it. Hope this helps. If you sear be careful. Burned garlic is no bueno.

Does the milk get rid of the ammonia taste/smell? And should it be soaked in the fridge or open air?

Yes and in the fridge. Anything left out more than 4 hours could make you sick.

If the shark has ammonia smell it is old. They go old fast and will get stanky, quick. I have caught many shark and they never smell sour until the next day. If you clean them and use or freeze they don't smell hardly at all. I wouldn't buy if smells like diaper, milk won't help. I am funny about seafood it is either my favorite of my least favorite food depending on how fresh it is.

Urea is present in the blood and tissue of sharks. It breaks down quickly, after killed, and it takes on a ammonia type odor. The more it breaks down the stronger the odor. IF the meat has been properly cared for, it can be soaked and cooked. I have also heard of using a mild flavored vinager or citrus juice to help remove most of the the urea. It is important to properly bleed the fish after killing to reduce this problem. I am very picky about my seafood, I worked in a seafood restaurant for 10 years. If it stinks, don't eat eat. Swordfish is better. Lighter and cooks up moist. Tuna awesome. It taste absolutely nothing like meat from a can. Good luck.
Fresh frozen is better than the stuff on ice in your supermarket. That stuff has already been defrosted and is quickly going out of its shelf life. Most filets/steaks are packaged in 5 lbs packages. Save and buy the frozen box. Most of it is IQF and you can seperate only what you need. I hope this helps.

That must be why sharks get that pissy attitude when you catch them...

Shark is great eating if cleaned right. But the first thing that should be done is bleed them out like it was said pryor to my post. As far as cooking them on the stove I cannot help you there. I marinade my shark in Italian dressing. Take it out of marinade place on the grill. Throw some lemon spices on it along with some seasoning and keep applying the marinade as it cooks. Cook up some celentro butter rice and put that fillet on top and go to town. Like all fish and game it is all in how you clean and prepare the meat as to how it will taste.

I have caught black tip shark, bled them while still alive, cleaned them, packed them on ice, and soaked the filets in buttermilk. I cooked the evening and it still stank like ammonia. I don't eat shark anymore.

i don't care for it personally, but make sure to fillet it and not stake it.

ok this may sound dumb but how do bleed fish?

Cut the sharks tail fin off to bleed them. If you can hang them it will be more affective. I do my big catfish this way as well.

To take this a little farther, the advice given is a must and I remove the tail, head to increase the bleeding-out of the shark and eviscerate them at the same time. Get the intestines out to take away the acid from the stomach from leaching into the meat. Ice heavily and get ready for some fine eating.