In Surgery, as far as I have experienced, every 5th year resident was a chief of whatever service they were on. A few were administrative chiefs who made schedules and organized, and they were selected by the PD and Chairman, people like that. This is announced in like the fall of the 4th year (so the chiefs for the following year). This helps for fellowships that have 4th year appointments as there is prestigue involved in being a chief. My program has 7 residents/yr though, and 3 administrative chiefs this coming year. Places that have like 2-3 residents/yr, all pretty much act as the administrative chief I would believe. Another place i rotated had 5 residents with 1 administrative chief and 1 other titled chief, I forget what exactly.
For Peds, IM, FM, the chief resident is one additional year that you apply for and then is selected by PD, Chairman. I don't know how many residents are in the medicine residency, but I know that they select 6 people to be chiefs (we have 3 hospitals they rotate through, and 2 chiefs per hospital including a VA, university hospital, and private hospital) I know at my host program, the Medicine Chiefs are selected during the 2nd year (so current 2nd year medicine residents know who will be chief resident for 2010-2011 year already) which makes sense because that is when many apply for fellowship and those wanting fellowship might not want to be a chief resident (although one big advantage of being a chief is it looks good on fellowship apps and for academic placements post fellowship).