To make compost tea you just need a covered container, compost, water, and time. I use a cotton pillowcase or a square of unbleached cotton. I move the bundle up and down a few times whenever I walk by the container.
More generally, the terms exergonic and endergonic relate to the free energy change in any process, not just chemical reactions. An example of an exergonic reaction is cellular respiration. By contrast, the terms exothermic and endothermic relate to the overall exchange of heat during a process.
Exergonic reactions are chemical reactions that release energy in the form of heat. Typically, this energy is released when bonds are broken. More specifically, in humans, these reactions are called catabolic, which means that the molecules are being broken down into smaller components.