It's all in the delivery
Mastering delivery can lead to you be great in almost any improv scene.
I study my funny friends on stage. Like Scott Patey, who was our special guest in Improv Against Humanity at the Vogue Theatre last night. I hosted, so I got to introduce and watch all of the inspired scenes. Scott can reliably delight an audience so I watch his trusted delivery methods. He has tried&true methods of delivering a line so that it produces laughter. Each of his characters is rich and three dimensional and they all know how to deliver a crisp line within the persona. So much of his unique comedic style comes from his delivery.
|That's Scott, delivering the middle finger as a corpse in a windmill full of corpses. Humanity!|
One of my improv teachers said to me "Being funny in improv isn't about saying funny things, it's about saying things funny."
My advice to new improvisors is to pay attention to the times the audience laughs at your work - when you can feel them on the same page as you. Try and remember the way you delivered the line. That "innocent response", that "last word", that "horny answer". These can become tools for your characters to use in future work. You'll get the feeling of good delivery, and you'll start getting good at delivery.
Also, pay close attention to the way that the ending of a scene sounds. You'll often hear that the final sentence completes the scene and wraps up the entire story. So it feels as if you've just swallowed the last delicious morsel of an epic piece of chocolate cake.