How did Tom get Ben to help in paint the fence in Tom Sawyer?

Tom convinced Ben that the "honor" and "opportunity" to whitewash a fence was something you didn't get to do every day.... something that was a bot of rare fun.

“Oh come, now, you don’t mean to let on that you like it?”

The brush continued to move.

“Like it? Well, I don’t see why I oughtn’t to like it. Does a boy get a chance to whitewash a fence every day?”

That put the thing in a new light. Ben stopped nibbling his apple. Tom swept his brush daintily back and forth—stepped back to note the effect—added a touch here and there—criticised the effect again—Ben watching every move and getting more and more interested, more and more absorbed. Presently he said:

“Say, Tom, let me whitewash a little.”

Tom considered, was about to consent; but he altered his mind:

“No—no—I reckon it wouldn’t hardly do, Ben. You see, Aunt Polly’s awful particular about this fence—right here on the street, you know—but if it was the back fence I wouldn’t mind and she wouldn’t. Yes, she’s awful particular about this fence; it’s got to be done very careful; I reckon there ain’t one boy in a thousand, maybe two thousand, that can do it the way it’s got to be done.”

“No—is that so? Oh come, now—lemme just try. Only just a little—I’d let you, if you was me, Tom.”

“Ben, I’d like to, honest injun; but Aunt Polly—well, Jim wanted to do it, but she wouldn’t let him; Sid wanted to do it, and she wouldn’t let Sid. Now don’t you see how I’m fixed? If you was to tackle this fence and anything was to happen to it—”

“Oh, shucks, I’ll be just as careful. Now lemme try. Say—I’ll give you the core of my apple.”

“Well, here—No, Ben, now don’t. I’m afeard—”

“I’ll give you all of it!”

Tom gave up the brush with reluctance in his face, but alacrity in his heart.