Aircraft that are already receiving an ATC service would normally report any emergency on that Air Traffic Control Unit's frequency. Most of the aircraft's pertinent details, prior to the emergency, should already be known to the controller, thus saving time.
Many aircraft, both civil and military, are not always in receipt of a full Air Traffic Control service. Should they get into difficulty, they can obtain rapid assistance from D&D (on 121.5 or 243.0 for military) who can 'fix' the aircraft's position using either radar or 'auto-triangulation'. Assistance with navigation and diversion is also available.