At this point, there is no instrument for measuring ki: nothing analogous to a barometer or thermometer or scale. The only measurements of ki are from human beings, self-reported, subjective and unverifiable. The phenomenon called "ki" may exist, but to say that you "know" it exists because your subjective sense perceives something that you choose to label in such a way, and that no outside source can corroborate, is a bit humpty-dumptying the definition of "know", IMO. Perhaps it's better to say that you believe it exists because you've felt something that you lack another explanation for. The problem with such beliefs is that they can become a little too firm, to the point of refusing to consider alternate explanations that are readily available.
When testing a student using a simple shoulder push I can feel when she goes from active muscular resistance to being moved to a state (we call correct feeling) where the force I am applying simply has no effect on her and she is able to stand stock still with little to no effort. The state of correct feeling is achieved when the student learns how to coordinate mind and body. Ki is manifest when correct feeling is achieved as a result of coordinating mind and body. Extend Ki is shorthand for the instruction "coordinate mind and body in order to achieve correct feeling." Once the student learns how she feels when performing this simple test she can then replicate that same feeling at will with other tests or when practicing technique.
The tests themselves also double as exercises that will help the student strengthen the connection between mind and body. With time and practice the student is able to handle greater and greater force loads (to a point of course, no Chevy pickups please). We refer to that as Ki development practice.
Knowing Ki exists is a matter of being aware of demonstrable differences in performance of certain tasks that can be performed with or without mind and body coordinated. The vocabulary used to describe the phenomenon is chosen because it's what I was taught when I began my training. As you can see from reading this and many other threads on AikiWeb, other folks use other words and methods of training to arrive at roughly the same place.