Remove the screen by detaching the screen clips with a screwdriver. Set aside the screen.
Open the window by turning the crank. Open it enough so you can comfortably reach three sides of the sash: the top, bottom and far side of the sash.
Remove the old weatherstripping. If it's been nailed on, this could be a challenge. If the material is pliable and you can pull it off without the nails coming out, then do so. If there are nails remaining, do your best to nail them into the wood or pull them out.
Measure each side of the sash that needs to be sealed. Unroll the adhesive vinyl pliable gasket weatherstripping. Cut sections of weatherstripping and peel away the backing.
Press the sections of weatherstripping in place along the side channels --- or just along the outside channel if installing along the inside channel will prevent the window from closing --- and along the top and bottom.
Open and close the window and latch it to make sure the weatherstripping doesn't prevent the window from closing. Adjust the weatherstripping as required.