It's obtained by scalarly multiplying the FIRST column of V_CKM by the complex conjugate of the THIRD:
V_udV_ub^*+ V_cdV_cb^*+ V_tdV_tb^*=0
The reason for choosing first and third is that this is the only choice that gives three terms of the same order of magnitude.
The angles α, β and γ are the arguments of these three terms, respectively.

All the three possible triangles have the same area, which is related to the degree of CP violation.

In the rescaled unitarity triangle, the global phase is chosen such that the second term (V_cdV_cb^*) is real, and all three terms are divided by its absolute value.
This way, two vertexes are fixed to the points (0,0) and (1,0).
The third vertex is floating: its coordinates are (ρ,η).

Wolfenstein parametrization:

ρ and η appear only in the third family: no CP violation with only 4 quarks.
λ~0.22 (cosine of the Cabibbo angle).

Extraction of CKM matrix elements:

V_ud: from nuclear beta decay.

V_us: from semileptonic kaon and hyperon decays.

V_cd: from νN interactions (νd->c).

V_cs: from semileptonic D decays.

V_cb: from exclusive and inclusive B decays.

V_ub/V_cb: from endpoint spectrum in semileptonic B decays. In fact, it is different if Q=m_b-m_c or Q=m_b-m_u, and from an inclusive measure one is sensitive to the u/c ratio.