Cut the top from the soda bottle. The hole should be just large enough to hold the Styrofoam cup. Make the cut level all the way around so the Styrofoam cup will sit evenly in the hole.
Cover the cut top of the bottle with heavy tape. This will both keep the sharp edges from cutting you or damaging the cup and help to hold the cup in place. Duct tape works well for this, but wide electrical tape can also be used.
Make holes in the bottom and lower sides of the Styrofoam cup by poking into the cup with a pencil or screwdriver. This will give the roots of the oregano plant a way to reach the water.
Put enough perlite in the cup to fill it most of the way full. Plant an oregano seedling in the perlite. Ensure that no soil is on the roots. If the seedling was started in soil, you can wash it off before planting it in the perlite.
Mix enough nutrient solution to fill the bottle. Hydroponic nutrients come in different concentrations, so follow the label instructions carefully to make a normal-strength mixture. Fill the bottle with enough of this mixture to reach the lower roots of the plant, but not so much that it covers all of the roots because they also need access to oxygen.
Set the cup into the opening on the bottle, and place it in a bright location. Your oregano will grow best if it gets at least six hours per day of bright sunlight.