Things which induce me to drop what I am doing and immediately get to work on someone's behalf:
1) Demonstrating that you know me well, either through familiarity with what I've done, what I've written, myself personally, or someone close to me.
2) Demonstrating that you have put a lot of work into something and can benefit from specific application of my expertise.
3) A precise request which I can satisfy. ("Can you teach me about running a business?" is not a precise request -- well, OK, it is, but only if you accept "I could." as a complete answer. "I have built an application which does X. I want to increase its organic search rankings for X, and having done my homework about SEO, I understand this means I need to get links to my website. Can you give me an idea for an X-related piece of linkbait?" is a precise question.)
Things which people frequently try that are not as successful as they probably hope:
1) "Help me, Obi Wan, you're my only hope." I enjoy backing underdogs, not losers. There is a difference. Pluck and vim and tales of what you've managed to do make you sound like an underdog. Apologies and lack of confidence and telling me who you've already asked who ignored you totally make you sound like a loser. (By the way, it very rarely improves any negotiation to tell the other party that they were the first person you thought of after the first four people you thought of said no.)
2) "This will only take..." Asking me to drop what I'm doing is much more disruptive than many people would assume it is. Also, folks have a tendency to underestimate how much work is required or how thoroughly I tend to answer requests which I answer.
3) Napkin stage ideas. Most of them will be culled before shipping. Why should I dedicate my limited time on a project which will probably be shelved, when I could instead work on something which will, with certainty, help people?