If the leader falls he will fall twice the distance from him to the last clipped anchor, this can be dangerous and must be carefully considered when deciding the distance between the anchors, especially on the lower part of the route. As the second climbs up he removes the anchors, the leader belaying him from the top. When the second reaches the belay he clips into the anchors and the two will rappel off the route or continue up the next pitch if the route is multi-pitch. Traditional lead climbing is when the climbers insert temporary anchors such as cams and stoppers into cracks on the route. The second climber removes these anchors as he ascends, leaving virtually no trace that they were there.
Sport climbing on the other hand requires that there be hangers bolted into the rock.
These hangers are permanent and should only be used when absolutely necessary, like when there are no cracks for temporary anchors, and when the route is not able to be top-roped. The leader clips quickdraws, two carabiners with a short length of webbing clipped between them, into the hangers and the rope into the carabiners as he climbs past them. Thus ends my very short overview of the process of leading a climb. I deliberately chose not to go into too much details because you really want to learn this with an experienced climber anyway. Meet activity partners for Climbing and dozen other sports.