Conveying information is a matter of figuring out what your audience currently understands, and what you want them to understand, and then charting a path from A to B. So the first thing I do is get a feel for where the audience is right now (by asking directly if possible, or making a best guess if not). Then I place myself in their shoes, and work backwards asking myself "why doesn't X makes sense yet?" to figure out which gaps need to be filled in.

To get more concrete: leveraging metaphors and bridging existing knowledge is a powerful explanation tool. If you're trying to explain X, and the audience already has a mental framework for Y which has some things in common with X, it can be much easier for both parties if you bridge from Y to X instead of constructing X from first principles.

Beyond just effectiveness of communication, this approach helps with the "condescension" factor too. One of the main things that makes someone feel stupid or belittled is when you explain something that they already know as if they didn't. So doing the up-front step of getting a good grasp on their starting point helps ensure that you're only telling them things they don't know already.