There isn't really a "click"-noise when putting them in, but push them down with a bit of force until they stop.
All you need is to drop it in. It does not require force as it will go in to place once seat is added/you sit on the seat. Also check your hand after installing as the top of the gas lift is a little oily, so you might want to wash your hands before touching anything else.
Align the hole and push it down. Be gentle as the seat is heavy and fingers might get in the way.
Note that you can adjust the width of the armrest here during installation. It is also possible to adjust the width of the top of the armrest after installation. See this page for instructions.
These two screws are pre-installed on the backrest. Push the backrest in and align them to the smaller part of the bottom hole in the seat mechanism. After, secure it by utilizing the two smaller screws in the accessory screw kit and tighten the lower pre-installed screws too:
The headrest/neck pillow can be lifted straight out after pushing the top button. Easiest way of getting it off again is by pushing the button and grabbing the top side of the headrest, as the mounts are further to the top than the bottom.
To find out more about chair functions and how to setup the chair, please follow this link.