Newton's second law deals with the relationship between the force, mass, and acceleration of an object. When using Newton's second law you look at all the forces acting on an object, add them up, and based on that determine the net force. The net force, combined with the mass of the object will determine the rate of acceleration.

When you are finding the net force there are two possible conditions: first, the sum of all the forces could equal zero. This means that the forces are in balance. In the case of walking a dog, if you are walking at a constant speed, that means that the force you are applying to the leash and the force the dog is applying to the leash are equal and opposite. So you are moving, but not accelerating.

The other posssible condition is that when you add the forces they do not equal zero. That means that some force is stronger than another force. In the dog walking case again, that could mean that the dog sees something of interest and runs toward it, jerking on your hand and arm and pulling you forward. In that case, the dog is accelerating. Or it might be that you see another dog coming toward you and want to get your dog closer so you pull on the leash, forcing the dog back toward you. The dog is again accelerating, but this time toward you instead of away from you.

This is a pretty vague question. But I will try to use Newton’s second law.

Newton's second law states that if a force F is applied to a body with a mass m, the body accelerates in the direction of the force by F/m.

When you take a dog for a walk, you would have to pull it sometimes by exerting a force on the string tied around its neck. This force will cause an acceleration in the dog which is equal to the force you apply divided by the mass of the dog.

Now the string is not pulled in a perfectly horizontal or vertical direction. It is pulled in a direction that forms an angle to the ground. The force can be divided into a horizontal component and a vertical component. The vertical component of the force acting upwards will lift the dog up slightly and the horizontal component will result in its accelerating towards you.