How to lock an inside door with round doorknobs turning both clockwise and counterclockwise (without a key)?
The lock/doorknobs look like the pictures. 


Does that mean the knob in the photo is not the actual door knob you have ? 

I am not sure about you door knob but on some older door knobs you push and turn to lock. It may be that it is only lockable with a key. 

Grasp the door knob that does not have the key slot in it, push the knob in and then while holding it in turn it, probably clockwise, just  little and it should stay in when you release it and that should lock it. 

You can do this with door open so you can test the other side to be sure it is locked.