Part 1
Chrisman34, what most people have a problem with is imagining that "draft" has something to do with the stove, or if they get past that, that "draft" is something constant produced by the flue (chimney).
Unfortunately, life is a bit more complicated than that. A chimney produces draft because warm air inside the flue is less dense than the surrounding air. Thats what you get when you heat air at a constant pressure - the density drops with increasing temperature. So, just like in nature where clouds rise off the sea from the sun heating the surface of the water, warm (or hot) air inside a chimney will rise through cooler more dense air around it. The difference is that by being enclosed in a chimney that is essentially insulated (and which, preferrably does not leak) it is possible to add up the boyancy of all the bundles of air in the flue and generate a much stronger draft than what is possible in free air where the flue gasses would be able to mix with surounding air. By mixing with the surrounding air, the temperature difference quickly vanishes and the bundles of air in the flue gas cannot combine their eforts to produce good strong draft. Case in point, most outdoor water boilers and BBQ's.
So now beyond the basic theory, one has to consider what is actually going on when you light a fire with a cold stove. The wood is cold, the stove is cold, the flue is cold as well as the air in it. If you have an inside chimney, the house itself has a "stack effect" since the air below the ceiling is generally the warmest, it is cooler on the floor and (at this time of year) it is quite a bit cooler yet outside. So if you had no stove, just the class A poking into the room (and an alternative source of heat) there would be a really nice draft rushing up into the class A, created by the difference in temperature between the air at the inlet of the class A and the outside air at the raincap multiplied by the length of the class A from begining to end. This is why, with a decent chimney, if you open the door of a cold stove it should start drawing air from the room into the stove immediately. If not, you have a problem.
So now you build your fire with kindling, small splits and 1 or 2 bigger splits. Light the kindling. Normally the draft is fully open and the door is cracked. The damper in your insert is really just a device to bypass the baffle, in other words, provide a direct path for smoke from the fuel to the chimney without doing 2 90 degree and 1 180 degree bends in the process. The draft at this stage is weak, because everything is cold, but to compensate we provide a lot of area for air to enter the stove to reach the fuel. This has the result that it "seems" like the draft is strong, since the flames flicker really strongly and you can hear the air rushing into the stove. NO, the draft is not strong, we have just deliberately provided it with unempeded flow to the kindling. The kindling in turn is fine, which means that it has a lot of surface area compared to its weight, so its volatility is high (in other words it can burn really fast). In reality, we are providing the fire with far more air than what it can consume. The best thing we can now do is to gradually reduce the airflow to the fire, keeping it just higher than what the fire needs to consume the wood. This will provide the greatest heat output from the fire. Some of this heat goes into heating the wood, some goes into heating the stove and the rest goes into heating the flue gasses.
The hotter the flue gasses, the more boyant, hence the stronger the draft. Over time the flue will heat up. Without having adjusted the primary air (and having earlier closed the door), the draft would become stronger and stronger. Within about 5-20 min (depending on dryness of the wood, size of the stove etc) a point will be reached where the stove will be in danger of overfiring unless we restrict the draft by starting to close the primary air. Initially reducing the primary air may cause the stack temperature to go up, since we reduce the excess air (not needed to burn the wood) thus also reduce the amount of air that must be heated. Further reducing the primary air will result in there being less air than fuel (rich) and the stack temperature will start to drop. If the baffle and the inside of the stove got hot enough (at least 600F), they will heat secondary air hot enough that it will spontaneously ignite any unburnt fuel (smoke) in the flue gas. That is why one sees the secondary flames. But secondaries will not happen if the inside of the stove does not get hot enough. Causes could be wrongly installed firebrick, no insulation blanket or firebrick on top of the baffle (generally has to be fitted during the stove install) or most common - wet wood.
Once the flue temperature is up to the 500 degree range (I'm talking a probe style thermometer, not a surface type) coming down off the back of the initial 700-800 degree burn, the draft should be really strong and you would need the primary air closed waaaaaayyyyyy down to maintain 500. If not, the fire is being cooled internally by steam (wet wood) or your chimney has so many leaks that you are totally diluting the hot flue gas with colder air that is being sucked in.
As the volatiles in the wood burn off, the temperature will drop. There will be little flame or sign of secondary combustion. This is normal. If you need a lot of heat, you can now start opening the primary air again to speed up the combustion of the coals which are almost pure carbon. Eventually, there should just be a fine white ash remaining and you sart back at the beginning.