A system is an object or a group of objects. When a system changes, the way its energy is stored changes. We describe this by saying which energy stores go down and which go up. The stores you need are the kinetic store (movement), the gravitational potential store (height), the elastic potential store (stretched or squashed objects), the thermal store (heat) and the chemical store (fuel, food and batteries).
Common situations are best described store by store. An object thrown upwards starts with energy in its kinetic store. As it rises, this is transferred to its gravitational potential store. A moving object that hits an obstacle loses energy from its kinetic store, and most of it goes to the thermal store of the object and the obstacle, with a little carried away as sound. A vehicle that slows down does the same: the brakes do work, the kinetic store falls and the thermal store of the brakes rises.
Energy can also move because of work. When a constant force accelerates an object, work is done on it and energy is transferred to its kinetic store. When a current flows in the heater of an electric kettle, electrical work is done and energy is transferred to the thermal store of the water until it boils.
Energy is not created or destroyed. The total energy of the system stays the same, so the sum of all the stores is the same before and after a change. In calculations we use joules (J) for every store, which lets us compare them on a common scale.