There's plenty of ways to approach getting a couple of signatures, but why not just use it as an excuse to get together with friends? Share a meal or enjoy the park! Whatever it is you do together, make it something that will allow you to talk—about what kind of system, what kind of change they think would be ideal.
In any case, get it out of your head that you're asking them for a favor. You're bringing them in on a great chance we all have to step up and take our power as sovereign citizens. There's no need to direct the conversation too much, but you'll probably want to have a decent understanding of what's being attempted. If you're really at a loss for words, here are some scripts.
If they follow your example and become links in this all city democracy chain, whom you pick could have a big influence on who else ends up being in on the conversation, so, for inclusivity's sake, try to include at least one person from a different social circle than whoever witnessed your signature.
Having an excuse to talk with fellow New Yorkers you don't know yet can be a lot of fun, too. It's our favorite part of this work, and you should feel free. Whether or not they'll be as likely to carry on and witness a couple of signatures themselves—and that resulting exponential growth makes all the difference—the less quantifiable rewards of such public conversations shouldn't be underestimated.
If you're having trouble, or would like to be part of a signature gathering team just let us know!