Classical conditioning was first developed by Ivan Pavlov. The way that this conditioning works is that a novel or neutral stimulus is presented first then the unconditioned stimulus is presented. This produces an unconditioned response. After x amount of trials the unconditioned stimulus when presented with the neutral stimulus becomes the controlled stimulus and the unconditioned response becomes the controlled response. There are many neural studies on classical conditioning when it comes to fear which have roles in learning and memory.
Positive reinforcement was used in operant conditioning where a reward is given for good behavior. For example: You get a discount on your car insurance for every 6 months you don't get into an accident.
Heres a video on positive reinforcement.