If you choose the former approach, then you should stick to the western wall of the canyon and make a beeline for the fence surrounding the base. George's note will give you two options: running through the destroyed town just outside the base, or using the train tunnel to the south (located between Raul's Shack and the Brotherhood of Steel Safehouse). Note: When you eventually return to George, he'll pay up as promised, but if you pass a Speech 60 check, then he'll give you 700 caps instead of 400/600. If you agree to this wager, then you'll receive the note 'Nellis Artillery Timing Details.' If you pay him 300 caps (or only 200 caps with Barter 40), then he'll tell you how to approach the base safely, and if you make it there and return to him, then he'll double your money. He'll tell you that the 'artillery-slingin' grenade-lobbin' odd-jobs' - aka the Boomers - who live in the base blow up anybody who gets too close to them, and he'll make you a wager.
If you approach Nellis Air Force Base from the road, then just past Fields' Shack you'll run into a gambler named George.