We have had a guest cat living with us for awhile and he brought with him some strange cat behavior.
One of the things he does is bite and claw at the cat food in the bag, even if the bowl is full.
I think its a game to him but it make a real mess.
He doesn't stop until he gets it open and spreads it all over the floor.
Now he isn't our cat but I figure he needs to live by our rules.
We could put the food up but we have two cats now and our cat Sid eats out of the bowl and we can leave the bag of cat food on the floor next to where we feed the cats.
It's convenient for us and that's how we like it, were the humans.
When training our Sid since he was a kitten we had certain rules in mind and those were the Cat behaviors we worked on teaching him.
These are cat behaviors we believe any cat in our house should obey(and Sid Does)

1. Eat the cat food out of a bowl and not the bag of food
2. Know it's name and come when called(at least most of the time)
3. Stay off of the sink
4. Use the cat box at all times

Don't bite the hand that feeds you When it came to the new cat Tabby, he needed some discipline so we started working with him after a period of time at least until we knew he felt comfortable in our home.
We used the same tactics that we used with Sid, since they worked pretty well with him.
There are many trains of thought for training a cat but this is what we did,

1. We use repetition when teaching him his name, call him a lot, and everyone be consistent.
   Don't use similar sounding words when calling your cat.
   Keep on until you get a response
2. Teach them the word NO.
   Again be consistent and get a response.
   Everyone should use the same word, not stop or don't do that, stick with the same word.
   
3. For biting use OUCH or NO and loudly.
   Make sure your not petting your cat to the point they have had enough.
   They will bite to tell you to stop.
   Sometimes they just want to sit on your lap.
   
4. We use a water bottle for really stubborn behavior.
   A quick spray and a loud NO will work very well.
   All we have to do now is pick up the water bottle if Sid is misbehaving.
   

With using all of the above we have taught Tabby to leave the bag of cat food alone and eat out of the bowl.
He has also learned to recognize his name much better and will come to me sometimes, all are huge strides since Tabby has been an outside cat and his inside manners needed some improvement.