Hunting High and Low (in Trees, That Is)

This week we learned about trees, yet again. But not just trees, binary search trees. We already know what a binary tree is. It's a tree where each node can have a maximum of two children. So then what is a binary search tree? A binary search tree helps us to find values efficiently in a set of data, without going through the whole tree/data! Well, how would that work? It works because of the way that binary search trees are organized. A binary search tree is organized so that everything less than the node is the left child/subtree of that node, and everything greater than the node is the right child/subtree of that node, starting at the root node. Binary search trees are greatly efficient when each node has two children. This makes sense because each time, half the tree is being is eliminated. But even though a binary search tree is supposed to be efficient, it doesn't always end up that way. For example, cases where each node has a left child, or where each node has a right child, end up being the same as going through the entire set of data, which is what we don't want because it isn't efficient!
It's clear why a binary search tree is an efficient way of searching through a set of data, but wouldn't the set first need to be set up as a binary search tree in order to search through it efficiently? If that is the case, how efficient would the process of converting a set of data to a BST be? If given a list of of data, one would simply insert the first element in to the tree as the root, if the next item was greater, the first item would become the left subtree of the new root and so forth and of course this would be done recursively. So it doesn't seem like it would be too hard!