How to open a door that has the insides of a door handle inside without a door knob
See the lock insides? That's a metal sleeve, with an inside sliding piece. That inside sliding piece is connected to the latch bolt. Push it to the left, and voila!



Some additional details. This is what you see when you remove the knobs, shaft and escutcheons from a knob set. The central shaft, which is has a flat, vertical cross-section, goes through that D-shaped hole. Turn a knob either way, and the top or bottom edge of the bar pushes against that sliding piece to open the latch. (Hence bib's suggestion of using a large screwdriver to act as that shaft.)

I believe the smaller hole on the right is for a lock. Push a button on the (interior?) escutcheon and a round shaft is pushed into that hole, preventing the sliding piece from sliding. Low-tech, but quite functional.