I'm not going to use any formulas!
Ok, those sounds you hear are the gasps of every physicist reading this. But they shouldn't be shocked. After all, back in the days of Newton and even today, physicists explain things by observing nature. Of course, they have to be more precise, so they model things with formulas. But we don't. So we'll put on our junior physicist hats and look at some things in nature.
So let's get started with the first law - inertia. There are two parts to this. If something is not moving and we don't do anything to it, it lays there like a lump. This is an interesting theory, and we'll need some intricate equipment to check this out. I'm proposing a hockey puck and a floor. We put the puck on the floor and watch. It doesn't just leap up and fly away. We've got to do something like kick it to make it move (although you better have good boots on or you'll hurt you toes).
To say this just a bit more clearly, to move the puck from its present speed (zero) to make it move to a new speed (not zero) requires force (the kick).
The second part of this says if something is moving and we don't do anything to it, it keeps moving in a straight line. We can see this law in action if we put that puck on an air hockey table. We give the puck a push, and it cruises along at a constant speed in a straight line until it hits something.
Actually, this really isn't any different than the first part. In this case, to move the puck from its present speed (not zero) to its new speed (something other than the speed it started with) requires a force (the cat who mysteriously jumped on the air hockey table and sat on the puck). That's probably why Newton only gave one law to these two parts.
That gets us to the second law - acceleration. This law says that if you want to change the speed of something you've got to give it a push. And, if you want to make the same speed change on something really heavy, you've got to give it a really big push.
So now that we're up to two laws, we can see how they work together. No matter what speed something is moving (and that includes our speed of zero) you need force to change that speed. Not only that, but that includes acceleration (making something go faster) and de-acceleration (making things go slower). Take away the force and the object moves along at the speed it was at the moment we removed the force.
In our scientific experiment for this law, we'll use a child's wagon and a car. It doesn't take much of a push to get the wagon moving, but the car is a different story entirely. Don't try this at home, but if you did, make sure someone is in the car to apply the force of the breaks to stop the car as the second law states, or the first law will say the car will keep rolling until it hits the neighbor's mail box.
That gets us to the third law - action / reaction. This just says that if you push on something, it pushes back on your just as hard. For this example, we'll observe the use of a gun by a highly trained law enforcement official. It's all I can do not to hurt myself typing on a keyboard.
So let's set this up. The gun is fired and a charge in the bullet explodes. The first question is why does the bullet comes out of the barrel in the first place? The answer is that the force of that explosion pushes on the shell (which is now part of the gun) and the shell pushes on the bullet. But if the two forces are equal, why does the bullet move so much and the gun so little (at least compared to the bullet)? The second law gives us the answer to that. The gun is so much heavier than the bullet, that the same force only accelerates the gun a much smaller amount.
I hope this unquestionably relaxed explanation of Newton's three laws of motion has made them understandable. And hey, if you want formulas, take a physics course - which is not a bad idea. It really isn't as scary as it sounds. That is unless your neighbor just put in a new mail box.