How do a pawl and a ratchet function together?

Quite well. A ratchet, which is actually the whole of the mechanism, has a gear (ratchet wheel) and pawl in it. Let's look inside and see what's there and how it works. The ratchet wheel is sort of like a "regular gear wheel" except that its teeth or cogs are cut with a sloped side and a "straight" or "offcut" side. That's in contrast to the two sloped sides of the tooth or cog on a regular gear wheel. Additionally, there is usually a curve in the slope of the "regular" side that acts as a ramp for the pawl to ride on. The pawl, which is usually spring loaded to keep it engaged with the teeth, will, when the ratchet wheel is rotated in one direction, slide up or "climb" the slanted or sloped side of a tooth. The pawl will then "jump" down into the bottom of the tooth space after going over the tip of the tooth, and the spring will have pushed it there. It will then ride up the next slope on the next tooth as the ratchet wheel moves in the same "forward" direction. But if the ratchet wheel is rotated in a "backward" direction, the pawl will only allow movement until it comes in contact with the "straight" side of the next tooth back, and it will jam there. This will limit backward movement of the ratchet wheel to a tooth length and no more, as long as the pawl is acting normally to check the backward rotation. There is no requirement that either the teeth or pawl have a given "cut" or "straight side" except that the ratchet wheel and the pawl, working in concert, will serve to jam the mechanism when an attempt is made to turn the ratchet in the "backwards" direction, and will allow free movement when turned in the "forward" direction. The ratchet mechanism is used in tools of the same name (ratchet). We've probably all seen them if not actually used them. The ratchet has sockets which can be slipped on a (usually square) drive of the tool so the setup can be used to turn fasteners. The ratchet mechanism is also applied to mechanical jacks which are used to lift vehicles for tire changes by the roadside. It is also applied as a pulling or lifting machine (the so-called come along winch) or in the tightening mechanism for cargo straps that truckers and aircraft loadmasters rely on. Wikipedia has a nice post on a ratchet showing the ratchet wheel and pawl. You'll find a link to that post below. There is also a link to an animated display of the function of the mechanism.