Read today's Times piece about her tenure as governor, and you'll see that two of her signature achievements involved giving away money. One was signing a $200 million increase in education spending, and another was approving a $250 a month subsidity to low-income elderly Alaskans; Palin had originally sought to restore a subsidy, cancelled by her predecessor, to all elderly Alaskans who had lived in the state since before its statehood. This of course was all made possible by the state's skyrocketing oil revenues. It's not that hard to become popular when you can fling around money like that. (Although this campaign is putting a dent in that popularity among Alaskans.)
P.S. On NPR this morning I heard an interesting description of her management style from a former newspaper editor who had worked in state government under Palin: "She governs by BlackBerry," he said, eschewing long substantive meetings. How reassuring. At least she doesn't use an iPhone.
--Michael Crowley