How does losing a turn work in Arkham Horror?
Short Answer: Being lost in time and space means that during your next turn, you skip all phases, including Upkeep. The only exception is during that same turn's Movement Phase, you simply stand up your token.

Long Answer: Here is the text on what happens when lost in time and space (core rulebook, pg. 17):


  Any investigator who is lost in time and space is immediately moved to the Lost in Time and Space area of the board. The investigator is now delayed, and the player should place the investigator marker on its side. The investigator loses his next turn, remaining in the Lost in Time and Space area. The player may only stand his investigator marker back up during the Movement Phase. On the following turn, at the start of the Upkeep Phase, the player may move his investigator to any location or street area of his choice in Arkham.


So the order is as follows:


Immediately go to the Lost and Time and Space area and become delayed (place your character sideways to mark that, as usual).
During your next turn, stand your character up during the Movement phase as normal for being delayed. As an extra rule for Lost in Time and Space, you skip all other phases (this is what is meant by "lose your next turn"). There are no encounters you can take anyway so skipping the Encounter Phase is moot, and there is no Upkeep phase (good if you want to stay Blessed, bad if you were hoping for income from a Retainer). This is confirmed by a topic on the Fantasy Flight Arkham Horror forum.
During the Upkeep phase of the following turn, you move your investigator to any location or street area in Arkham and continue with your turn as normal.