Had mine done through the NHS. Basically two questions, "do you have children already" and "how long since your last child was born?".
If you haven't had kids yet, you just need to explain why you want a vasectomy, usually with a specialist. If your last child was born less than two months ago, they want you to wait (apparently a lot of men's first reaction to the realities of having a baby is to try to ensure it won't happen again).
Even imagining this pronunciation hurts my ears.