In the first Matrix movie, we see that red-pills can exit the Matrix by picking up a phone and calling the operator:
However I don't seem to recall if it's ever shown how they enter the Matrix, from the perspective of the simulation. Do they just pop out of thin air? Do they spawn from the same phone booths? Is it ever shown on the screen?
It is never shown on screen.
On The Matrix (1999) it is almost shown, they pop up all around a ringing phone (which one of them answers with "We're in"), but we never actually see it directly, since the camera is spinning showing the room, and on the next spin the whole group is there. So in the time it takes to make a spin around the room, it loads 7 red pills (Morpheus, Neo, Trinity, Cypher, Switch, Apoc and Mouse).
On The Matrix Reloaded, the closest we have is when Trinity attacks the Power Station. We see her on top of a building, with a Ducati (apparently) away from any phone, but it's hard to tell if she just spawned there with the bike, or if she got up there by some other means. It does make it seem like she spawns with the bike, because the bike is stopped/standing still, and she does a burn out, and by the dialogue about the lack of time. If she had gotten there by other means, she probably wouldn't have stopped the bike for the jump.
We do know they can be "loaded" with items of choice, as we see in Matrix 1 and their "Guns, lot's of guns" scene, so I'm guessing she was loaded in with the bike.
