I enjoy hearing what people are doing for living, what they spend most of their hours on, and usually they ask in return. So it happens that I get to pitch to almost every new person I meet. And also to people I haven't seen in a long time.
I usually prepare about 3 explanations of what I'm building (pitches) and choose on the spot which one I pitch right now. The results are interesting, I can usually tell after 10-15 conversations which one is better.
Then I create 2 more and test the current 3 options.
When doing that I highly recommend hearing their story and what they do first. You can then try to spice your pitch with elements that they can relate to.
For example, if I learn that my conversation partner has a child with ADHD then I can spice it with my personal story, or if I know that they are an electrical engineer then I can connect it with a skill they might want to learn ("VHDL, FPGA) if I know something about that field.
How do you present your project to new people?
Like the idea of creating multiple pitches ahead of time. I'm doing the same while submitting my product to online sites. Feedback isn't as clear as in-person, but I can at least compare which pitch converts better.
Also like seeing how my more mature competitors explain it on their sites & blogs.