Look carefully, and you will notice that a faction is a lot like a character. In Edgerunner, you can play whole factions just as you play characters. You can even build a game around factions, and never involve a single character sheet in your game, keeping the story mechanics on a grander scale and only going down to the character level for narrative flavor.
But remember that this game is about edgerunners, and those are singular people with a whole lot of personality. Though it may be fun to play the clash of the titans every now and then, the more interesting stories always involve real characters that you and I can relate to.
Not to mean that those characters can't get involved (or possibly crushed) in a clash of the titans.
As players, your primary agent in affecting the game world are your characters. However characters are always limited in what they can do. They can't change the future, and they cannot move mountains. At least not by themselves, not directly. It takes a faction to do that.
Factions can create or stop progress, they can spawn or destroy other factions. Characters cannot do that all by themselves. They need a faction to do that for them. As a player controlling a single character, you do not normally have access to factions. The referee controls all factions involved, unless you use one of the mechanisms below to control a faction.
There are four ways for you as a player to take control of a faction, and almost all of them involve using your character at some point.
If you are playing a [corporate] character, then you also have a faction under your direct control. You can just play the faction as it was another character. You also get to receive the fate points when your faction is compelled.
If your character has defined his affiliation to a faction with a dedicated upgrade, then you may take control of the faction for the duration of a single scene or conflict, by spending a fate point. The referee can refuse this by giving you a fate point instead.
When a character takes out a faction, the character's player can choose to assume control of the faction for the remainder of the conflict, and for one single action following the conflict. Be careful with the narrative though. Taking a faction out does not mean that they capitulate and obey your character's commands. It only means that they somehow are forced to act in a way that is in your interests as a player. If you can't tell a plausible story, then you probably can't make the faction do that.
This is the usual game mechanism, no more. You can just compel a faction through an aspect, in order to get it to act in a certain way. Of course the controlling player(referee) can refuse the compel as in the rules, giving you a fate point.
These are the four game mechanisms for getting a faction to act in a certain way. However, do not forget the rule zero of Edgerunner: You can narrate anything any time. If everybody at the table likes your story, then it happens. No need to use any game mechanism. That holds true for any and all factions as well.
There are two different types of conflicts that factions may find themselves in. Faction vs. faction and faction vs. characters. The first case is played mostly like any other conflict, where factions attack, move, maneuver and do all the other conflict actions on a map. The only major difference is that the map usually does not represent physical space but an abstract space such as political standing, or research progress that the competing factions are going after.
When the map in faction vs. faction conflict represents physical space, that space is usually much larger than what is represented in character conflicts. The zones may be city neighborhoods, whole cities or even countries. But in this case, it usually does not make sense for the factions to move about, unless they are roving gangs or similar. Assume the faction exerts its maximum influence in a certain zone (which probably begins where its base of operations are) and let the faction affect every zone on the map, subject to range from this focus zone. The faction may "move" this focus to other zones, thus changing range to its targets, but as a target itself, it always resides in its original zone. Moving this base of operations should be a major undertaking, and it may or may not make sense in the scope of the conflict you define, especially considering the length of an exchange. When you consider it possible, make sure that moving the focus is easier than moving the base.
In a faction vs. faction conflict, remember that the Influence of involved factions are applied to their competency rolls
Characters have no effect in a faction vs. faction conflict. But if the story of an action in such a conflict involves the characters, you may opt to break into a sub-conflict involving the characters, whose outcome determines the results of the action in the bigger conflict. Evaluate the results of the small conflict and assign it an adjective on the ladder, from the perspective of the acting faction in the larger conflict. Assume that to be the number of shifts the acting faction obtained.
When a faction is involved in a character conflict, it is not represented on the map. It may only take a maneuver action targeting the entities on the map, or use the special deploy action to put various human and tech resources on the map to fight on behalf of itself.
The deploy action allows a faction to spawn characters and tech on a character-scale conflict map. Roll an appropriate competency. Shifts allow you to place a new character or tech at the far end of the deployment map. Full characters require 8 shifts for deployment, extras and goons require 6 and 4 shifts respectively. Mobs require shifts equivalent to double their threat level minus one. Deploying vehicles and other technology takes enough shifts to cover double their cost.
The deploy action is assumed to be targeted towards characters, so the faction's focus is in full effect as a modifier.
The required shifts are deliberately quite high. A faction has a number of options to make deployment at character scale possible. It may maneuver and accumulate aspects to invoke, which means it is taking steps to prepare the asset for deployment. It may also take Leverage stress and/or consequences to cover some of the shifts needed. Or it may simply continue the deploy action. Continuing a deploy action increases the previous result by +1, eventually generating enough shifts to put the asset on the scene.
If successful, the deployed asset appears on an appropriate entry zone on the map, ready to act on the next exchange.
When a deployed asset is taken out, any unabsorbed stress overflows to the faction as Prestige stress. Wasting assets looks bad on you, so remember that a strategic withdrawal is the prudent option when circumstances call for it.