Choose an area of the greenhouse that receives at least six hours of light during the day. Coat the glass of the greenhouse with tinting film or place the olive sapling near the center of the room and away from the windows so the foliage does not burn.
Plant an olive tree sapling in a large, well-draining pot, covering the roots up to the original soil line with potting soil. Water until the top inch of soil feels damp when you push your finger into it. Keep the top inch of soil moist, watering more often in hot weather and less often once the weather cools and the water does not evaporate as quickly.
Apply a balanced fertilizer around the roots of the tree every two weeks during the growing season. Cut back on the fertilizer and apply it only once a month during the dormant season.
Prune your olive tree if it becomes too large for your tastes or the greenhouse. Prune each limb back to a growth point with sharp pruning shears. This should only be done at the end of the dormant period, in the spring just before the new growth begins.