Empty the aquarium and clean it with soapy water. A clean terrarium will grow grass better than one full of leftover fish scum. Scrub the sides with a clean sponge or rag to remove the remaining dirt and let it sit in the sun to dry for a few hours.
Pile enough gravel or pebbles in the bottom of the aquarium to cover it, but do not build up the layer too much. A 1/2-inch to 1-inch coat of pebbles will serve as the bottom level of filtration.
Place a layer of charcoal over the top of the pebbles. You can find this at a plant store, or use old aquarium filters broken up in pieces. Again, do not build up the layer too high as this is a lower level of filtration but not a primary growing layer.
Put sphagnum moss on top of the charcoal. This will serve as a bed for the soil and will enrich the roots of the grass plants.
Place soil on top of the moss. This layer should be built up a few inches so the roots of the grass plants can grow deep enough to support a taller plant.
Plant the grass seed in the top layer of soil by sprinkling the seeds on top and gently pressing them into the soil. Do not cover the soil with a thick layer of seeds; leave enough space for the seeds to germinate.
Set the aquarium in a place that receives partial sunlight and rotate it every few days so the grass does not grow slanted into the sun. Do not place it in direct, all-day sun as the glass sides of the aquarium will raise the heat and you could scorch the young grass plants.
Spray the seeds with a light mist of water from the spray bottle every twelve hours while the aquarium sits in the sun. The glass sides will incubate the interior of the aquarium and provide a lot of heat for the seeds, so they must be misted often to maintain hydration.