Analyze. Prepare. Cheat.
Analyze:
Do your players deviate from the module in predictable ways? What regular habits do they have? What deviations cause you trouble? Frex, some folks start fights with noncombatants. Some wander away from the dungeon and head off into unexplored territory. Some like to talk when the adventure expects them to fight. All of these situations may require you to improvise.
Prepare:
Try to anticipate and prepare for deviations your players are likely to take. If they like to start fights, prep extra statblocks. If they like to wander off, prep a few quickie side trecks (the DDI Chaos Scar adventures are good for this). If they like to talk, take a few minutes and think about any NPC's they might want to talk to: their goals, motivations, etc. etc.
Cheat:
Use Seventh Sanctum and similar random generators in game to come up with names, motivations, etc. for NPC's.
Reskin the monsters in published combat encounters and use them for impromptu battles.
Listen to your players' table talk and then make their speculations reality. If a player says, "maybe there's a tribe of angry goblins behind all this." Then by god, there is a tribe of angry goblins behind all this.
Steal plots and characters from movies, comic books and cheesy novels. It might be hard to improvise dialog for "a fighter" its a lot easier to improvise dialog for "a fighter who is basically Owen Wilson from Bottle Rocket."
Analyze:
Do your players deviate from the module in predictable ways? What regular habits do they have? What deviations cause you trouble? Frex, some folks start fights with noncombatants. Some wander away from the dungeon and head off into unexplored territory. Some like to talk when the adventure expects them to fight. All of these situations may require you to improvise.
Prepare:
Try to anticipate and prepare for deviations your players are likely to take. If they like to start fights, prep extra statblocks. If they like to wander off, prep a few quickie side trecks (the DDI Chaos Scar adventures are good for this). If they like to talk, take a few minutes and think about any NPC's they might want to talk to: their goals, motivations, etc. etc.
Cheat:
Use Seventh Sanctum and similar random generators in game to come up with names, motivations, etc. for NPC's.
Reskin the monsters in published combat encounters and use them for impromptu battles.
Listen to your players' table talk and then make their speculations reality. If a player says, "maybe there's a tribe of angry goblins behind all this." Then by god, there is a tribe of angry goblins behind all this.
Steal plots and characters from movies, comic books and cheesy novels. It might be hard to improvise dialog for "a fighter" its a lot easier to improvise dialog for "a fighter who is basically Owen Wilson from Bottle Rocket."