Law the First:
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.
This means that, to change an object's velocity (or lack thereof) a net force needs to act on it. This happens...anywhere, really. Your chair stays where it is because the gravitational force is negated by the reactionary force of the floor (see third law). An aircraft gets continually faster as it's taking off because the thrust from the engines is larger than the drag caused by the air (until it reaches cruise, anyway). Basically - if the forces on an object don't completely cancel each other out, the object will accelerate.
Law the Second:
The acceleration of an object is dependent upon two variables – the net force acting upon the object and the mass of the object.
F = ma, as the poster above me stated. Going back to the aircraft example, a piston engine on a Cessna can accelerate the aircraft at a certain rate, reaching some velocity after a certain amount of time. If you tried to use that same engine and propeller on a 747, it would take much, much longer to reach that same velocity (ignoring drag, friction etc).
Law the Third:
For every action, there is an equal and opposite reaction.
Basically, when two objects interact, an equal and opposite force acts upon each of them. Take the chair example from earlier - your chair is exerting a force on the floor. To stop that chair from just going straight through the floor, the floor exerts a reactionary force back on the chair which is equal in magnitude but opposite in direction, creating (in this case) a net zero force. A bird pushes on the air in flight, pushing the air backwards, but the air also exerts a force on the bird's wing, pushing the bird forwards.
Does that help at all?
(BTW, credit should be given to http://www.physicsclassroom.com/Class/newtlaws/newtltoc.html" for the definitions. It goes into each of these laws in much more detail and was found on a Google search of "Newton's laws", amazingly enough. That crazy internet can do anything these days!)