C.R.
From age 1-2, babies are developmentally going through an exploration phase and learning about the world around them. This is very inconvenient for the parent, but important for the child's development. I agree with Lori's methods for making this easier on you, but try not to discourage their experimentation or they will learn not to explore or question things (very important for later success in life). Meal time is a favorite time for this kind of 'exploring' and William Sears actually recommends just putting a tarp down and letting them make a mess and then wait until they are done to clean it up. Believe me, the novelty eventually wears off if they are allowed to satisfy their curiosity. Punishing with a negative tone is never a helpful tactic, as it only creates insecurity.
With dogs and kids, any kind of intense emotional reaction is a huge incentive for them to do it. This is not out of rebellion or "testing" -- it is actually biologically ingrained for them to keep soliciting the reaction -- i.e.,they can't help it! So with any behavior you are not excited to see over and over, it is always best not to show too much emotion around it. Matter of fact and calm are better reactions.
From ages 2-4 ('two'-berty) their primary developmental goal is to find out ways in which they are a separate being from the parent. This is why "no" is their favorite word. Again, you don't want to punish this developmental stage (they are driven to do it no matter what) but allow them to feel in control by giving them choices and allowing them to make small decisions themselves. Discouraging their attempts to assert themselves as separate beings from you only hurts their sense of self and independence.
Remember, toddlers are not little adults and don't benefit from being forced to act like us right away. Gentle teaching and repetition without expectation of immediate results will yield far better results down the line than punishing or creating battles -- believe me, toddlerhood is NOT the hill you want to die on. I've read that you need to gently repeat things over and over and over and at around 3 they start to assimilate the information and actually act on it.
So, to recap, (roughly) age 1-2, babyproof and control the environment, not the child. They are learning the laws of physics, how things work, and practicing their muscular skills. Age 2-4 (and beyond), give choices and allow as many safe and nonessential opportunities as possible for your child to be 'in control', making choices, and asserting themself. This will lead to better behaved children and more empathetic adults!
Paul Holinger's "What Babies Say Before They Can Talk" has lots of valuable child development information that is important for all ages.
Any of Dr. William Sears' books are user-friendly, good ways to keep your parenting on the right track.