Old Grognard here: I grew up with The Avalon Hill Game Company, and was one of Simulation Publication Incorporated’s best customers.
Wargame: start with a map with a grid. A hexagonal grid is very common.
Counters: little half-inch cardboard squares to represent units. You can stack them together, to represent a concentration of forces, or you can spread them apart, only one counter per hex, to represent a light “screen” of defending troops.
This, by and large, is the whole key to the game: where do you concentrate force, and where do you let your forces be thin.
(In real life, allied forces in Europe in WWII spread themselves very thin – and the Germans punched right through them, creating the “bulge” in the Battle of the Bulge.)
Movement: the counters can usually be moved a limited distance. If you’re going to concentrate a bunch of units, you want to be prepared by having them all close enough to the concentration point to reach there in one move.
Combat: usually done by counting up odds. Each counter usually has an Attack Strength and a Defense Strength. Say, a U.S. Tank Division has an Attack of 12, a Defense of 10, and a movement of 8. A German Tank Division might have an Attack of 13, a Defense of 9, and a movement of 8. If the “American” player can concentrate five of his tank divisions to attack on enemy tank division, the total odds are 60 attack to 9 defense. This rounds down to “6 to 1” which is a very good attack ratio.
There is usually some die rolling at this point. At high odds, the results are very likely to be “Defender Destroyed.” The defending counter is removed from the map.
At low odds, the attack might succeed…or it might not. The attacker might end up getting destroyed. (This happened in real life in the Crimean War…rather a lot.)
The game is a contest of maneuver, and of concentration of force. And also of some luck.
These games are somewhat historically accurate. They tend to have outcomes that could have happened in real life. So, for instance, in these games, Japan almost never wins WWII…but sometimes they can make the war last longer. The battle of Midway could have gone differently. The battle of Waterloo could have gone differently.
The games are educational. You can learn a lot about what actually happened. You learn a lot about geography from studying the maps. You learn the very basic rudiments of maneuver, tactics, strategy, planning, and even deception. If you can make the other guy think you’re attacking his left…and you actually attack his right…you can win the game.
The games are abstractions. In real life, units that lose a battle aren’t “removed from the board.” They usually are scattered, but rally and get back into action in some way. The simplification makes it a better game.
The games are primarily for entertainment. They’re more realistic than chess, but they can’t be taken as true historical simulations. They’re an awful lot of fun, and I’m very sorry that the hobby collapsed so heavily back in 1974. (Dungeons and Dragons killed it dead!)