What's the process for an uncontrolled airfield to become controlled/towered?
I finally found an AOPA article that discusses requirements for a control tower.

They say:


  The FAA has the authority to establish control towers or discontinue
  control tower services through the National Airspace System when
  activity levels and safety considerations merit such action.


In order to open a new tower, there must be a positive Benefit-Cost ratio (which is a complicated thing to calculate).  The FAA typically pays for the cost, and here is the criteria that they list:


  Criteria
  
  According to FAR Part 170.13, the following criteria, along with
  general facility establishment standards, must be met before an
  airport can qualify for a control tower:
  
  
  The airport, whether publicly or privately owned, must be open to and available for use by the public as defined in the Airport and
  Airway Improvement Act of 1982;
  The airport must be part of the National Plan of Integrated Airport Systems;
  The airport owners/authorities must have entered into appropriate assurances and covenants to guarantee that the airport will continue
  in operation for a long enough period to permit the amortization of
  the control tower investment;
  The FAA must be furnished appropriate land without cost for construction of the control tower; and
  The airport must meet the benefit-cost ratio criteria specified herein utilizing three consecutive FAA annual counts and projections
  of future traffic during the expected life of the tower facility. (An
  FAA annual count is a fiscal year or a calendar year activity summary.
  Where actual traffic counts are unavailable or not recorded,
  adequately documented FAA estimates of the scheduled and nonscheduled
  activity may be used.)
  
  
  The FARs specifically state that an airport is not guaranteed to
  receive a control tower, even if the airport meets all the criteria
  listed above. This is where the contract tower program comes in. The
  FAA, responding to an airport sponsor's request for an air traffic
  control tower, can elect to establish a contract tower. The FAA can
  either elect to pay for the service in its entirety, or enter into a
  cost-sharing agreement with the sponsor, depending on the results of
  the benefit-cost analysis. Typically, the airport sponsor is
  responsible for 10 percent of the cost of construction and operations.


For the Benefit-Cost calculation, they use the following criteria:


  Site-specific activity forecasts are used to estimate three categories
  of tower benefits:
  
  
  Benefits from prevented collisions between aircraft.
  Benefits from other prevented accidents.
  Benefits from reduced flying time.
  
  
  Explicit dollar values are assigned to the prevention of fatalities
  and injuries and time saved.
  
  Tower establishment costs include:
  
  
  Annual operating costs: staffing, maintenance, equipment, supplies, and leased services.
  Investment costs: facilities, equipment, and operational start-up.
  


The article contains a lot more information, along with links to the relevant regulations, etc.