US Citizens DO require a visa to enter Turkey.
Presuming you are only visiting for tourism (which it sounds like you are), you can obtain the Visa (the "sticker" you refer to) at your point of entry. After you enter the airport but before immigration there is a window where you simply hand over the visa fee and they will put the Visa into your passport. You then proceed to immigration who will stamp the sticker.
The visa fee varies depending on your nationality, but when I was there a few years ago it was US$20 for most countries, more for Canadians (US$80 I think) and a few other countries.
There's no interview/forms/etc involved, it's really nothing more than a "pay the fee and get your visa" setup. The visa is good for 90 days.
You can also obtain a visa in advance from the Turkish consulate, but unless you're going for more than tourism there's really no point.