What's the fastest way to find the Kth smallest value in an unsorted list without sorting?

Question

My initial algorithm:

1. Compare element 0 with every other element, keeping track of how many elements are less than it.
2. Repeat for each element until an element that is greater than exactly (k-1) elements is found.

I assume this would take $O(n^2)$ in the worst case. Can a faster runtime be achieved without sorting the list?