(covers information from several alternate timelines)
A promotion was an honorable upgrade of a rank.
In Starfleet, in the 24th century, the promotion ceremony involved pinning the pip of the new rank on the officer's collar by their commanding officer, or some equivalent thereof. (DS9: "The Adversary"; Star Trek IV: The Voyage Home; Star Trek Into Darkness; TNG: "Lower Decks"; VOY: "Revulsion", "Unimatrix Zero") The Deep Space Corps Selection Board was the Starfleet entity responsible for reviewing the eligibility of in-the-zone or above-the-zone promotion of an officer. (TNG: "The Measure Of A Man", okudagram)
In 2258, James T. Kirk was promoted to captain of the USS Enterprise by the Starfleet Academy Board, for saving Earth from Nero. Admiral Richard Barnett pinned a medal to Kirk's dress uniform to signify his new rank. (Star Trek)
In 2371, the senior staff of the USS Enterprise-D used a ceremony incorporated into an elaborate holodeck recreation of a 19th century sailing ship, for Lieutenant Worf's promotion to lieutenant commander. Commander William T. Riker indicated that this was a tradition for Enterprise senior staff promotions. This included having the newly ranked officer trying to grab an officer's bicorne hat hanging out over a plank. Worf was the first officer to not fall into the holographic ocean. (Star Trek Generations)
In 2374, on stardate 51186.2, Lieutenant Tuvok was promoted to lieutenant commander on board the USS Voyager during a promotion ceremony presided over by Captain Kathryn Janeway in Voyager's mess hall. (VOY: "Revulsion")
In 2377, Tom Paris was promoted back to lieutenant junior grade following a previous demotion to ensign. The ceremony took place when he started his duty shift to find a box containing his new pip at his station. (VOY: "Unimatrix Zero")
In 2380, Beckett Mariner was promoted from Ensign to Lieutenant in a scheme by Captain Carol Freeman to get her daughter off the USS Cerritos. The scheme failed and Mariner was demoted back to Ensign after insulting a Vulcan admiral. (LD: "Moist Vessel")