I've never asked for help on here before Emotion: stick out tongue

Anyway. How do I teach my lab not to jump on counters and steal food?

She's 3-years-old and rather stupid. She wasn't trained at all by her previous owners, and we think they used to feed her table scraps because she always eats like she's never had a meal before in her life. I can't get her to respond to any sort of training, even with treats.

This morning, she pulled a pan of brownies off the counter and onto the floor. Just now, she jumped up and ate some of the cake we just made!

She is absolutely crazy. She's eaten teabags, garlic cloves, peanuts, anything that she can find.

Does anyone have any tips for training a (probably mentally challenged) dog to not only stop jumping on counters but also stop stealing food?
Tricky one, since you're paying for the lack of training done by the previous owner.
Is it possible to keep your dog out of your kitchen during the time you are preparing food? Like this you'll be reducing the chances of it even happening and the dog gets less motivation to do it. My friend once set up a trap for her dog, used a piece of meat on a tray with some cans and marbles in it. Dog wants to snatch the meat but the tin comes crashing down and gives the dog a fright. It worked for her but am not sure if this is the 'friendliest' way to do it.

Don't give her any attention when she does it, she's getting double the gratification like that. Instead, praise her when she does let you prepare food in peace and does not snatch the food, and supervision is the key.
well since she wasn't trained by her previous owners it will take time. What i would recommend starting off with is teaching her the words "leave it" this should be said in a really harsh strict and slightly louder voice.
To teach her these two words is to start by using one of her foods and placing it on the ground and covering it with your hand completly but make sure she knows its there. The next step is when she tries to eat it say "Leave it!" Loudly harshly and scrictlly she should step back in supprise although she most probably will try agian you must repeat "leave it!" agian just louder. You have to keep this going all the way untill she finally backs off and sits down. Or in your case just one of those should be good enough.
Now that she has sat down and backed off you have to reward her by giving her a treat and telling her the words "take it" happily so that she knows she did some thing good. But when you give her a treat, DO NOT give her the one you told her to leave, if you do she will take it as anything she leaves will eventually be fed to her anyways.
Practice this everyday and when she starts to leave it and sit down right away then try doing this again but this time after she sits and backs away lift up your hand and say leave it just less harsh and mean. If she goes for it quickly cover it again and say as harshly and loudly as possible "leave it"
This method took me a month to train my puppy with, but since your dog is already grown and not trained before it will take longer. It's very important to remember to be patient or she she will feed off of your negative energy and become frusturated. I know one more method but usually only works with small puppies. Please tell me if this works! I would love to know if it doesnt tell me and you can try the other method.
Also for the time being try to keep your dog in her cage or in another room while preparing food.
@Raphael, the problem is we cook all the time. It's a household hobby. She's quite alright when we're actually cooking, but as soon as anyone has their back turned, she makes her move. And if we don't give her attention, she'll eat the entirety of whatever it is she's snatching..

@Taffy N Fatty, I have tried that Emotion: sad she's insanely fast. As soon as you put food down, she's gobbled it up before you have time to even pull her back. She doesn't have a cage, and like I said, we make food all the time.

I'll try what both of you suggested, though! I'll have to be more patient with her, I suppose.
hmm... yea if you've tried before and it hasn't worked i'm not complatly sure what to do. Sorry, just keep practicing and be patient!
That must be extremely frustrating! How is it going lately?