I just signed up for this testing window via phone, so here's my experience in case it helps:
I called them up, gave them my name (and verifying info like e-mail and address), and then they asked "Okay, so when do you want to test?" I mentioned a week in which I wanted to test (ie, sometime between May 14 and 18) and they read me a list of open dates and times for that week. I chose one. It was quite easy, and I got an e-mail confirmation.
I think (think, don't know) that back when the test was on paper, rather than on the computer, there were only a few test dates per year. But now that it is computerized, you have more or less your pick of days within a given monthlong window in which to take it.