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.
An endergonic reaction (such as photosynthesis) is a reaction that requires energy to be driven. The activation energy for the reaction is typically larger than the overall energy of the exergonic reaction(1). Endergonic reactions are nonspontaneous. The progress of the reaction is shown by the line.