Well - if it is new, one end of the buckle would already be attached to the leather. So, the next step is easy.
My apologies to Angus for stealing this from his site - but, just to illustrate. See the other end of the buckle, on the bottom left corner of the pic? The head can pivot on the bar attaching it to the rest of the deployant, yes?
Well, pivot the head on the axis of the bar so that it is perpendicular to the piece that says "stainless steel". This should now give you enough space to slide the leather strap in. Assuming your buckle is in the same orientation as the pic above, you slide in the tip of the strap from the bottom left, towards the top right.
The two studs found on the other side of the head will be pushed into one of the strap holes, once you hae adjusted the length to fit your wrist. Sorry, don't have a video, but hope this helps.