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 they are allthe 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.