Neo being jacked in.
The process of Jacking In involves the connection of a redpill's headjack to the communication network of a hovercraft so as to materialize within the Matrix or Construct as an avatar.
To jack-in, the crewmember sits in a chair, and their limbs are strapped in to prevent movement as a safety precaution. The operator then inserts the jack data connector into the crewmember's headjack. Normally, the crewmember appears to lose consciousness, when in fact their consciousness is relayed into the avatar that forms moments before in the artificial world or world-space.
A crewmember's consciousness must be carefully disconnected from a construct area from the operator console and using a proper hard line within the construct world, or instant death will result.
Only humans that originated from the Matrix can access the Matrix, which leaves Zion-born (naturally born) humans, who have no headjacks, to serve on hovercraft to serve as operators or other support crew.
Behind the scenes
While the movies have shown clearly the effect of the moment a user disconnects from the Matrix (the avatar dissolves in green sparkles), they have never shown on screen how an avatar pops up or materializes in the Matrix at the moment a user jacks in.