Q: How can I be sure I am paying the right amount when I send my lift?

A: I will assume you are talking about less than a full container (LCL). If your shipment was in consolidation or groupage (these are both terms referring to a container with two or more shipments) then you will be paying by the cubic meter or cubic foot.
You have every right to take a tape measure and measure. Multiply the height (from the floor!) by the width and by the depth to get your cubic measurement. Verify this is the cubic meters or feet you are charged.
Be warned, correct measurements in the shipping business are far too often incorrect. I will be gentle when I only say, I have never seen a mistake to the advantage of the client.