According to Jehovah's Witnesses, when/how do the 144,000 ascend to Heaven? Following an invitation, I attended a "Memorial of Jesus' Death" service at a Kingdom Hall recently.  While there, I heard about the 144,000 who will go to heaven to "be kings and priests and rule over" those who remain in earthly paradise.  How/when does this happen?
This is from the perspective of Jehovah's Witnesses.

The how and when of the 144,000 being gathered is answered by Jesus' illustration of the Wheat and the Weeds described at Matthew 13:24-30, 36-43:


  24 He presented another illustration to them, saying: “The Kingdom of
  the heavens may be likened to a man who sowed fine seed in his field.
  25 While men were sleeping, his enemy came and oversowed weeds in
  among the wheat and left. 26 When the stalk sprouted and produced
  fruit, then the weeds also appeared. 27 So the slaves of the master of
  the house came and said to him, ‘Master, did you not sow fine seed in
  your field? How, then, does it have weeds?’ 28 He said to them, ‘An
  enemy, a man, did this.’ The slaves said to him, ‘Do you want us,
  then, to go out and collect them?’ 29 He said, ‘No, for fear that
  while collecting the weeds, you uproot the wheat with them. 30 Let
  both grow together until the harvest, and in the harvest season, I
  will tell the reapers: First collect the weeds and bind them in
  bundles to burn them up; then gather the wheat into my storehouse.’”
  
  ...
  
  36 Then after dismissing the crowds, he went into the house. His
  disciples came to him and said: “Explain to us the illustration of the
  weeds in the field.” 37 In response he said: “The sower of the fine
  seed is the Son of man; 38 the field is the world. As for the fine
  seed, these are the sons of the Kingdom, but the weeds are the sons of
  the wicked one, 39 and the enemy who sowed them is the Devil. The
  harvest is a conclusion of a system of things, and the reapers are
  angels. 40 Therefore, just as the weeds are collected and burned with
  fire, so it will be in the conclusion of the system of things. 41 The
  Son of man will send his angels, and they will collect out from his
  Kingdom all things that cause stumbling and people who practice
  lawlessness, 42 and they will pitch them into the fiery furnace. There
  is where their weeping and the gnashing of their teeth will be. 43 At
  that time the righteous ones will shine as brightly as the sun in the
  Kingdom of their Father. Let the one who has ears listen.


Here's an info-graphic from a 2013 Watchtower article - “Look! I Am With You All the Days”



How

Angels will harvest (or "reap") the wheat class of anointed Christians, bringing them into Jesus' storehouses. These storehouses represent the restored Christian congregation. They are then brought to heaven in these ways:


Anointed Christians who were already asleep in death at that time are resurrected and begin ruling with Jesus in heaven.
Upon the death of an anointed Christian after the harvest has begun, they will immediately be resurrected to their position in heaven, “in the twinkling of an eye.” (1 Cor. 15:52)
Anointed ones which live all the way up until the great tribulation will receive their final sealing shortly before Armageddon and be brought to heaven invisibly (note that Jehovah's Witnesses don't use the term “rapture,” because it has a connotation of happening visibly).


When

The harvest season “is a conclusion of a system of things,” which began in 1914. Anointed Christians have been gathered into the storehouses of the congregation since 1919, and the exact times of the Great Tribulation and Armageddon are at some unknown time in the future.