How to open this locked door

If you have the doorknob - look at the back of it and see how it actuates.

I'd suspect theres a vertical bar that rotates, and pushes on the top or bottom black bit, making it move to the right in the photo.

You can probably duplicate that action with a screwdriver, put the tip where the letter A is, and push the tip to the right.

That type of latch rotates (there is a half-cam inside) That square hole you see is engaged by the shaft on the missing knob, and rotates that piece. You can use anything to turn that either way. A screwdriver with a bit too big to fit straight, but will fit in 'diagonally' will do the trick... a quarter turn should open it fully.

This is provided it is the same as the kind I am trying to describe, from what I can see in the picture.

Also, after you get in, when you try to put the pieces back together, make sure the key works BEFORE you close-up and lock yourself out. It is often possible to get the inside knob and outside knob together wrong by 90º, and then you will probably not be able to rotate the key one direction, and/or be able to turn the lock-tab inside both ways. Check the knobs and keys and lock tab function, with the door open, for proper operation BEFORE you close the door...

Hook into the metal bit (red in my picture) and push it to the right.

The red piece is the end of the latch bolt. pull on it an the bolt retracts. the cam that normally pulls on it is missing