Storm window frames don't allow window-mounted air conditioners to tilt forward to the outside. When the air conditioner doesn't tilt forward, it won't drain properly. Using a level, half a bubble will be enough for proper drainage. Air conditioner manufacturers sell kits for installing air conditioners in regular windows, but you must make simple modifications to install it in a storm window.
Measure the distance from the interior windowsill to the bottom storm window frame opening and add 1/2 inch.
Measure the length of the windowsill.
Cut a piece of 2-inch-wide lumber as long as the measurement in Step 2 and rip it to the height of the measurement in Step 1.
Attach the piece of wood securely to the sill with appropriate screws. You will have created a mounting to compensate for the artificial lip created by the storm window.
Attach the top-mounting rail strip. Remove the backing and attach it to the top of the air conditioner case with included screws. Install the side accordion panels too with screws. Cut the window sash seal to the window width and stick it adhesive side to the bottom of the sash.
Install the case in the window. Attach the sill supports to the fabricated 2-inch wood strip you've added, rather than the window sill itself. Secure the case and install any support brackets. Add a window gasket to fill the gap created by a half-raised window. Slide the air conditioner into the case and screw it in place.