You should use Triggers to achieve this.
Create a new GameObject to represent the trigger area. Choose the most appropriate shape. This will be the area that you have to enter in order to cause the teleport to occur.
Now select the new object you just made, and tick the "Is Trigger" option in the collider component, shown in the inspector pane. This changes the collider from a solid object to an area that you can walk into.
Un-tick the "Mesh Renderer" component, so that the GameObject becomes invisible.
You probably also want to specify a destination for the teleporter, and an easy way to do this is to create another invisible GameObject. This time however you don't need a collider either, so it's best to use "Create Empty" to create a completely empty GameObject. Name it "Teleport Destination".
Now, depending on how you want the teleporter to work, you need to either add some script to the teleporter object, or to the player object.
If you want the teleporter to teleport any object which enters it, add a script something like this to the teleporter object:
var destination : Transform;
function OnTriggerEnter(other : Collider) {
other.transform.position = destination.position;
}
If you only want the player to teleport when it enters the trigger, you should make sure your player object is tagged as "Player", then add a check for this in your teleporter script, making it look more like this:
var destination : Transform;
function OnTriggerEnter(other : Collider) {
if (other.tag == "Player") {
other.transform.position = destination.position;
}
}
See the Colliders Manual Page for more information about triggers.
Now for the camera. If your camera is parented to your player (as it is, in the case of the first-person controller prefab), then you need do nothing. The camera will be moved along with the player automatically.
If you're using a chase-style camera however, you'll probably want to make the camera jump the same relative distance as the player just jumped. You could do this by measuring the distance that the player moved, and then adding that distance to the camera too - something like this:
var destination : Transform;
function OnTriggerEnter(other : Collider) {
if (other.tag == "Player") {
var startPosition = other.transform.position;
other.transform.position = destination.position;
var moveDelta = other.transform.position - startPosition;
Camera.main.transform.position += moveDelta;
}
}