You must go, in person, to a French Foreign Legion recruitment station. They're located in certain town across France. Getting yourself there is your responsibility, but once there if everything goes...
Well the first step is of course, one must apply for and obtain a French visa, buy a return air-ticket to France with own money and reach there. Once in France, present themselves at one of the many...
Yes, of course. According to the Foreign Legion's wikipedia entry, about 1000 American citizens have been incorparated in the Foreign Legion. There's no restriction to enter the Foreign Legion except...