Knowing how to come up with new stuff on the fly, but also knowing what is appropriate to make up and what not to do, in a accordance with the game style and setting.
One of the trickier aspects of larping is that we’re never playing in a completely defined setting, our characters are always full of holes we have to fill in ourselves. This requires improvisation, the ability to make stuff up as needed.
There are three main places improvisation takes place: During character creation, when prompted ingame and when you need to bring in new stuff yourself.
Whether you are to play a prewritten character or make up your own from scratch, you have to build it from a starting point defined by the organizers and make it align with their intent. This means you improvise the details within a framework, but you have the luxury of getting it checked by them before you play.
When the game is on, you’ll invariably end up in a situation where you are asked a question or have to relate to something you haven’t thought of before, there’s rarely time or opportunity to check with an organizer, so you have to make up your own content.
Sometimes the game is going in a wrong direction for you or you run out of stuff to play on, so you need to find a new way forward, this also calls for improvisation.
Improvisation is as easy as lying. You just make something plausible up. The trick is not be creative here. The first rule of improvisation and lying is to be as obvious as possible, don’t invent anything fancy. The thing that comes to mind first is often the best to use and most likely enough for your co-players.
Different kinds of larp takes different amounts of improv, some have very fixed lore that limits what you can bring in, others require that you invent large amounts yourself. Try improvising as you play and take notice of the responses you get. As you practice more, you’ll become better at sizing your improvisations to different larp situations.
In general you should know if the thing you improvise would be known by others in the game, if not, you pretty much have free hands. Otherwise some moderation is good. Don’t state your new idea as absolute fact, but treat it as real memory: Sometimes its faulty or plain wrong.
Improvisation is fun, you probably already do a lot of it when roleplaying. If you want some more advice, Play Unsafe http://theunstore.com/index.php/unstore/game/49 by Graham Walmsley is the best book on roleplaying improvisation out there. For a real deep look, the books on theatrical improv by Keith Johnstone http://keithjohnstone.com/ are the cornerstone itself.