Air conditioners are set in the window with a slight angle so the unit leans backwards for the water to drain out the backside. On top of the air conditioner unit is a top mounting rail. The window closes on the backside of the rail to hold the unit in place. When the window is closed, the unit is somewhat secure in place.
The air conditioner installation kit has accordion inserts for the left and right side of the unit that open up so that each accordion meets the side of the window frame. The accordion inserts attach to the unit by sliding the accordion into the slide on the side of the unit. Inserts attach to the window frame with screws. If the accordion inserts cannot be secured with screws, tape can be used to hold the inserts against the window frame.
Once the accordions are secure and the window is closed down on the top mounting rail as far as it will close, the window locking bracket is screwed onto the top of the window and the window frame to prevent the window from opening. If the window frames are vinyl and you don't want to make holes in the frame, a board the size of the opening from the top of the window to the top window frame can be put in place to prevent the window from opening accidentally.
Air conditioners differ in size and weight. If you have a 12,000 British Thermal Unit (BTU) air conditioner and feel the weight will be too much for your specific window assembly, you can use a mounting bracket that the air conditioner sits on while in the window. Mounting brackets attach to the windowsill with screws and have a brace that sits against the side of the house on the outside.