The USCF's USchess.org has a post by GM Larry Kaufman, co-winner of the U.S. Open chess960 side event, GM Kaufman on Fischer Random & The Irvine Grind, where he described the method of selecting the start positions.
In this event the method used was to have the youngest child present point to one square after another while the TD drew pieces (other than Rooks and King) at random from a bag. It's not a purely random method as the child could in theory use strategy to try to get positions he liked, but it wasn't a problem in practice.
Since this method could easily end with two Bishops starting on the same color square, I assume a tweak is needed. The Kaufman post links to a long USchess forum response by Gene_M (Gene Milener, author of 'Play Stronger Chess by Examining Chess960'): USCF Forums > Chess Life Articles > GM Kaufman on Fischer Random. He writes,
For masters a completely unfamiliar setup is too complex for them to play strong chess during the opening phase. Chess960 must be narrowed to exactly one non-traditional setup, for at least a decade. From studying the annual FRC-chess960 Rapid tournaments in Mainz... We have learned that we have already learned all we are ever going to learn from Fischer's version of chess960. A change is needed. Schmidt and the ChessTigers.de organization should announce one non-traditional setup that shall be the only setup to be used in cooperative chess960 tournaments for the next decade (until at least 2020).
It escapes me why Milener undermines the main reason to buy his book, but he is in good company. Garry Kasparov is on record for having said similar; see Kasparov's Chess960 Proposal. Worth noting is that the two co-winners at the U.S. Open event were the two top players. Is the statement that masters can't play unfamiliar positions perhaps not accurate?
GM Alexandra Kosteniuk posted a piece about the Mainz simul on her Chessqueen.com blog: Kosteniuk Chess960 Simul. One of the photos is a screen shot of the final results. The last two columns identify the start positions for each of the 20 games (translating from the German): SP222 NQRKNRBB, SP444 RBNNQKBR, SP666 RNKNBQRB, & SP888 RBQKBRNN. For some reason, this list doesn't match my records for the same SPs, which are 223, 444, 555, & 888, respectively. The fifth and sixth columns on the same chart show some kind of rating, where we see that many of GM Kosteniuk's opponents were rated above 2000. Whatever start positions were really used, the final result of +16-0=4 again contradicts Milener's hypothesis about unfamiliar positions.