That depends on what the pet is. A cat bonds differently than a dog, for instance.
I find the best way to bond with dogs is through positive reinforcement (ie little to no punishment) training. Training a dog to a high level in any canine sport or endeavor develops the deepest bond a human can experience with an animal.
Of course, any dog trained to a high level in a canine sport should also already be experiencing the usual bonding methods of house dogs such as petting, grooming cuddles, play, etc. :)
I bonded with my cat by simply carrying him around on my shoulders, which he loved. Also just letting him sit on my lap for pets bonded him to me. I also trained him to do tricks, but that didn't especially increase our bond as cats are very different than dogs. :)
Other pets such as horses, sheep, guinea pigs, etc. will all need different bonding practices based on their species.