NOTE: All of the following is based on sources outside the series, and so may not be canon, or could be contradicted later. This is a purely speculative attempt to reconstruct 'Tahiti' using "The Avengers" and similar information.
Agent Phil Coulson was killed by Loki Laufeyson, the "god of mischief" just prior to the Battle of New York. He was aboard Director Fury's Helicarrier, and was assigned to guard the prisoner when the vessel came under attack. He was carrying a prototype weapon, a S.H.I.E.L.D. design directly consequent to the encounter with Thor and Loki a year earlier.
Loki used his powers of illusion to make himself appear to be at the control panel for the cage, then skewered Coulson from behind with a Chitauri scepter. After he sent his step-brother plummeting earthward confined in the cage, the mischief-maker turned his attention back to the dying agent and his final words, beginning with, "You're gonna lose." Coulson proceeded to demonstrate Loki's "lack of conviction" but putting his last reserves of energy into discharging his weapon at the god.
Coulson's action kept Loki from taking full advantage of S.H.I.E.L.D.'s disarray, and the Asgardian made his escape with his cohorts. Director Fury found the last vestiges of life in his friend, but they were already slipping away. Coulson's final words were, "This was never gonna work if they didn't have something to..." The concept may have inspired Fury to "mislead" Captain America and Tony Stark into believing that Coulson had, in his final moments, been carrying his "Captain America" card collection, looking to get Steve Rogers's signature.
Technically speaking, Fury doesn't say at the scene that Coulson is dead in so many words. His first pronouncement is, "Agent Coulson is down", followed by the announcement that the medical team, "called it". Later, he declares, "Phil Coulson died still believing in that idea. In heroes." Speaking to Maria Hill concerning the deception of the cards, Fury's justification is, "They needed the push." This suggests there would be no automatic limits to how far he would go to motivate the Avengers. Agent Hill, unlike the superheroes, knows of, and knows all about, Coulson's return.
There have been numerous indications, beginning with Agent Hill and Dr. Streiten's conversation in the "Pilot" and including the stingers to "The Hub" and "The Well", that Tahiti is not what it seemed, and may well be an implanted or heavily modified memory, to mask the true nature of Coulson's revival.
Most of the outstanding points connected with this theme were addressed in "The Magical Place". However, in "Providence", Agent May states that Fury did not personally oversee Project T.A.H.I.T.I., reopening the can of worms.
In "Nothing Personal", it is revealed that Coulson himself oversaw Project T.A.H.I.T.I. when it was intended to save "a mortally-wounded Avenger", and stated to Fury, in his report recommending the termination of the experiments, that only memory replacement had shown any hopeful signs of averting mental breakdown or psychosis due to an awareness of what was done. Sadly, when Coulson found out about the truth of T.A.H.I.T.I. he began to show signs of mental breakdown similar to John Garrett's.