In book form, the equivalence of the Coxeter and Bernstein presentations of the affine Hecke algebra appears in the first 4 chapters of Macdonald's book "Affine Hecke algebras and orthogonal polynomials". It is very carefully written, but the notation can get a bit heavy. When first reading it, I suggest you always assume that you are in case (1.4.1) in Macdonald's notation.

Chapter 5 does rank one examples.

In book form, the equivalence of the Coxeter and Bernstein presentations of the affine Hecke algebra appears in the first 4 chapters of Macdonald's book "Affine Hecke algebras and orthogonal polynomials". It is very carefully written, but the notation can get a bit heavy. When first reading it, I suggest you always assume that you are in case (1.4.1) in Macdonald's notation.

Chapter 6 does rank one examples.