How do you standardize recurring business processes across a team?

Every month our finance team goes through the same close process but if you ask three people how they do it, you'll probably get three different answers. It works fine until someone's on holiday. Then the person covering spends ages asking where files are, which report comes first or who normally signs things off.

I'm trying to get everything into one consistent process before it becomes a bigger issue. How have you handled this without making documentation overly complicated?