Luckily there are two rules that are always true with sewing machines, but you have to look closely to check the first one.
Simple rule #1: The flat side is nearest the hook.This one requires you to look at which side of the needle the hook is on. In Singer 66 and 99 the hook race is very large, and the hook actually passes the needle on the outside. That is, the hook is to the right of the needle. Following simple rule #1, that means we have the flat on the right.
Models 66 and 99, the hook is to the right,
so the flat is too.
Model 201, smaller race means the hook
is on the left, so the flat is too.
Simple rule #2: Thread also goes toward the hookThat means the thread always exits the needle on the hook side.
Vertical bobbin machines are a bit harder to see, but as soon as you see the hook, you know how to put in the needle and how to thread it. This will maybe save you a lot of time looking for manuals.