Make your offerings incredibly specific - actions with great detail, dialogue that provides multiple specific details for the scene. If everyone else in the scene is listening, they have a greater chance of taking those specifics and running in the same direction as they were offered. If you enter the scene as Charles the cop, there are many ways the next player could take that - as a fellow cop, as a criminal, as a lawyer, etc. But if you enter the scene as Charles the cop who stares you down and says, "I expect you know exactly why I pulled you over," that gives the scene much greater focus - and suggests to the other players who they can become to help drive that scene forward.
Such specificity can often be challenging, because many players - particularly high school players - will take that as a sign of "Oh, so-and-so is going to lead the scene." Thus, more junior players (ones with less experience or less confidence) will often not make such a specific offer. The exact opposite is true - if you want to help yourself out in a scene with a stronger player, give that player a strong offering to go with. If they're listening and playing to the top of their game, they'll give you back something you can be confident working with. The only way to build experience and confidence is to jump in and do it.