How to convert from standard form to vertex form when a is not 1?

Excuse me, could you elaborate on the process of converting a quadratic equation from its standard form to vertex form, specifically when the coefficient of the squared term (denoted as 'a') is not equal to 1? I understand that in standard form, the equation is written as ax^2 + bx + c = 0, but how do we manipulate this to find the vertex and express it in the form y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola? I'm particularly interested in the steps involved when 'a' is not unity.