“How you mount your horse can set the tone for a safe, effective ride. Here’s how to get both you and your horse started on the right foot, complete with instruction from trainer Steve Stevens.”
Here is a great instruction video on mounting safely.
I agree with Steve’s methods here, except for the part about reaching down to get your off-side stirrup. I feel it’s best to have your stirrups “trained” correctly so you can pick it up with your foot without reaching over.