When a dogs gets wet, it shakes its body from head to tail to shed the
water. Explain this is Newtons first law of how this works?

Dogs are extremely intelligent, but they just can't talk to tell us
all they know about physics, so Newton gets lots of credit for putting
into words what any wet dog knows.  Dogs suffer from the frustration
of their verbal limitations  - which may or may not have anything to
do with the expression:  "It's a dog's life."

"Newton's first law of motion is often stated as
An object at rest tends to stay at rest and an object in motion tends
to stay in motion with the same speed and in the same direction unless
acted upon by an unbalanced force."
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1a.html

So what every good dog knows is that by shaking his body he sets in
motion the water in his hair, which by Newton's law then still
continues in the same direction when the dog shakes in the other
direction, the drops of water flying off in  - more or less -  the
original direction of their motion.