There is a small but very good monograph, devoted to extreme points of compact sets:

Robert R. Phelps Lectures on Choquet's theorem. Lecture Notes in Mathematics 1757

You can find a number of applications of Krein-Milman theorem in that book.

Also there are some good applications in Walter Rudin's Functional Analysis, say

in the proof of the Stone-Weierstrass theorem, or in the description of C*-algebras.

There are also some theorems about existence of extreme points without the compactness assumption. See in the book

Benyamini, Yoav; Lindenstrauss, Joram Geometric nonlinear functional analysis. Volume 1.

the chapter devoted to the Radon-Nikodym property

Thank you