The only thing a player needs is Discord https://discord.com/ , for giving out orders and communicating with other players. Umpires require Tabletop Simulator
https://store.steampowered.com/app/286160/Tabletop_Simulator/ in addition to it, to be able to oversee the scenario via the umpire table. Owning TTS can be helpful as a player, as it allows the player to freely view the map on their own, but it is not required, as umpires can provide them with a picture of the map.
Usually, the game consists of 20 minute turns, divided into a 10 minute player-turn, and a 10 minute umpire-turn. During the player-turn, umpires via discord send their player(s) a time-update (1 turn is often 15 mins in-game), a screenshot showing what the player sees, possible courier messages they've received, and a report of anything noteworthy, like the sound of musketry far west, or a battalion being slowed down by difficult terrain. The screenshot, showing the player's point of view, is taken from the umpire-table by the umpire. The umpire simulates fog of war by limiting the information shown in the screenshot by simply bordering the picture, zooming in or out. The player's point of view is restricted by the terrain around him, if he moves himself and his staff on a tall hill, he might see the enemy formations in the distance. As the firefight goes on, his view of the battlefield is gradually reduced, as the thousands of muskets being fired cover the battlefield in smoke.
Towards the end of the 10 minute player-turn, the umpire requests any possible orders the player has. Then the game proceeds onto a 10 minute umpire-turn, where the umpires execute the players' orders according to how troops realistically would perceive them, how terrain would affect movement, seeing which units are running low on supplies etc. Couriers are sent on their way, and any combat is progressed. Most games tend to have one umpire per two or three players to keep the game smooth.
The role of an umpire is quite popular, as it allows one to appreciate the battle unfolding from a bird's eye-view, and gives experience that might come to use if one wishes to host their own scenario.
Counting both players and umpires, the Grand Gettysburg -game had actually 50 participants in total.
Most of our games are quite lengthy sessions, our largest game, Grand Gettysburg, lasted 7 hours. 90% of the players played till the end though!
We also host play-by-post games, similar to PBEM-games, where games last for several weeks, and turns can take entire in real life days.