Have the smallest adult do the installation; there isn't much room to maneuver. LATCH does not apply on aircraft; you can't use that method.
If it is an infant seat, don't bother with the base because it probably won't work, either, due to the position of the belt buckle.
On the aircraft seat in the window position, raise the armrest, put the seatback to full recline, and pull the buckle on the seatbelt out to the fullest extension, leaving an inch or so of belt to grab onto. Thread it through the belt passage on the carseat, and twist the buckle one half-turn before you latch it, so that the latch mechanism of the buckle will not end up pressed against the seatback. Then push the carseat into position and draw up the slack on the plane's lapbelt until it (on a toddler carseat) disappears into the carseat channel and tightens up. Lastly, pull the aircraft seatback to the upright position so it tightens against the carseat. (You probably will not be able to lower the armrest with the carseat in position.)
If you have a seat that uses a belt path that runs directly behind the child's back inside the shell, ask the FA to provide a seat belt extender. Add it to the seatbelt and adjust the length of the two pieces of belt so that you don't end up with the lap belt buckle sitting directly in the small of the child's back.
If you cannot get the seat undone when you land, wait for the passengers in the row behind you to leave, then recline the seat again, go around to the row behind, and reach up between the cushions to release the belt buckle.