Instead of asking how to help, review their goals, industry, hiring, life events and news, then show up with something specific.
The idea
Better questions beat "How can I help?", and the best help of all needs no question. You know what would help because of what you've already learned about them, or can look up on the fly. Most people don't announce their needs; they hint at them.
How to do it
Before you reach out, run through:
What goal did they mention the last time you spoke?
What's most valuable to someone in their industry or role? (Agents always want better marketing ideas; CEOs want leadership insight.)
Is their company hiring? Check the job board or website.
Any life event: wedding, new baby, new town, new role or company?
Any bad news lately about their company or industry?
What project are they in the middle of?
Pick one thing you can do about one answer, and offer it specifically.
Example
Brad Lambert, now a Hollywood producer, told me this one. As a college freshman he was friends with Willy, a Steelers running back who broke his leg near the end of the season he was leading the NFL in rushing, costing him a six-figure bonus and the title. Willy had money, family, a house. Brad couldn't give him anything he lacked, except the one thing Willy couldn't do himself. Brad spent about two months making calls, and Willy and his family ended up spending a game with his idol, Michael Jordan. Brad's rule: don't go in with your hand out. Treat them like a normal person and offer value.
Watch out for
Research online, never in real life. Don't "happen to bump into" someone because you worked out where they'd be.
Better Than "Anything I Can Help With?": Retire "How can I help?" and "What's up?" Ask about their biggest challenge, what you'll celebrate a year from now, or who they want to meet.
Listen for Their Ask: People hint at what they need in passing. Capture their "ask" after every conversation and offer help before they think to request it.
Five-Minute Web Reconnaissance: Spend five minutes on someone's profiles and posts before meeting them. Aim for familiarity, and stop well short of stalking.
The Biggest Fan: When someone you care about launches something, picture their fears and show up like a marketer would: buy, share, and post the first review.