A typical encounter in Aftermath! goes like this: Our player, let's call him Mad Max, enters a cave at the edge of a ruined city. In this cave, Max finds a man who's been making his living scavenging food and supplies from the ruins of the aforementioned city. Let's call our scavenger Bob.
The game master rolls to determine Bob's reaction to Max. The Reaction Table is consulted. Bob's reaction is "bad" - he is not happy that his home has been invaded. We now enter Detailed Action Time (DAT), or, in other words, combat.
The DAT display (a hex map) is brought out. Max places his figure where he stands; the GM places Bob. The DAT display is used to judge the line-of-sight and side or rear attack penalties. Let's say Max and Bob are facing each other, so there are no penalties. The Range Table is consulted to determine whether or not Max's weapon, a .357 Magnum revolver, can hit Bob. As it turns out, Bob is relatively close to Max, within 20 meters, meaning he is within the "effective" range of Max's revolver. Max is all set.
The order of battle is pre-determined. Each round is broken into "phases" during which each player will act. The player with the highest Base Action Phase goes first. Max has the higher BAP in this instance. He decides to shoot Bob. He rolls a 20-sided die. Max is rolling "against" his own skill with the revolver. If he rolls below or equal to his Base Chance for Success with a pistol, he hits Bob; if not, he misses. Max's roll is equal to his BCS. He hits Bob. Hooray! But wait, there's more.
In each situation there may be one or more "modifiers" to the player's BCS. We must first consult the Situation Modifier Table to determine if Max is doing any of the various things that will modify his score, such as kneeling, running or attacking in poor light. Max is doing none of these things, but there is a "distraction" present - our cave is filled with smoke from a nearby fire. This will distract Max, hindering his ability to fire his weapon accurately. The amount of distraction is up to the GM, so let's say our smoke introduces a penalty of one point. This point is added to the Max's roll, meaning he has rolled higher than his BCS. Max has missed. Max is sad. But wait, we're not done.
We've forgotten to consult the Inherent Accuracy Table to determine if the type of weapon being employed adds any modifiers (carbine rifles add +3 to hit). Let's say Max is using a pistol with a "standard" length barrel. This gives him a +1 bonus, subtracting one point from his roll, meaning he once again has succeeded. Max is happy again. But we're still not done. The GM will now subtract Bob's Overall Defense Ability from Max's roll to hit. Bob's ODA is 1, which, when subtracted from Max's roll, means Max has again missed. Shoot. But wait! We forgot that Bob is sitting down! Max caught him eating his dinner of scavenged canned ham. This gives Max a two-point bonus to his attack roll. He hits! Hooray!
Having hit his target, Max now makes another roll and consults another table - this time, the Hit Location Table. The result of this roll indicates where Bob is hit. In this case it's the 4 location, the upper right chest. Now if Max has enough skill points in the use of a pistol, he can "aim" by relocating his shot however many points along the opponent's body. Max has a high enough skill score to aim by two points, so he moves his shot to Bob's 2 location - his face. Brilliant! We now consult the Bob's armor sheet to see how much armor he has at that location, but he has none, because, well, it's his face, and also, he was eating dinner. Can't do that with a face mask. (If he were wearing armor there, however, we would consult another table to determine how much damage the armor itself takes, and whether or not it's destroyed and therefore unsalvageable.) So, Bob has taken a round from a .357 Magnum full in the face with no protection. We must now determine how badly he is hurt. It's time to consult another table.