Most class experiments involving the greenhouse effect utilize carbon dioxide, because it is easier to obtain, transport, and work with. However, some of these experiments can be modified to work with methane, if it can be safely obtained. Remember that Methane is extremely flammable, odorless, and highly toxic if breathed in large quantities.
The standard greenhouse gas experiment uses two or more identical, transparent sealed containers, one filled with a standard atmospheric air mixture (opened, shaken to normalize the internal air, and sealed), and one (or more) containers with additional CO2 added (larger amounts in more containers for a larger data set). Replacing the CO2 with methane should allow for similar results. Once the containers are sealed, they are exposed to a powerful lamp generating heat for a period of time, during which the internal temperature rise is measured by a thermometer left inside the container. A piece of dark material, such as a piece of coal, will help with internal absorption and radiation of heat. The theory is that the heat from the lamp will remain inside the containers at a specific level; reflected by the transparent container, the heat will reflect around the medium of the atmosphere before dissipating over time. A container with larger quantities of methane should retain more heat as the extra medium prevents dissipation.
With the proper tools and personnel, this experiment can be performed by middle- and high-school students to show the effects of greenhouse gasses on atmospheric temperatures. Remember to read up on the differences in handling methane and CO2, and adapt the experiment accordingly; also, care should be taken that the containers do not expand during the heating process, as they could explode and cause harm and damage. The links below describe similar experiments in more detail.