Perhaps as this is a ninth grade science class, your book/teacher is breaking things down into simpler "bites". However, some clarification may be in order.
There are only six general types of energy:
Electrical (or electro-magnetic)
Of these, Mechanical is generally subdivided into Kinetic Energy (the energy an object has by virtue of its motion), stored Gravitational Potential Energy (the energy it has by virtue of its position away from a gravitational body), and stored Elastic Potential Energy (the energy it has by virtue of a stretched or compressed medium).
Any given material object is comprised of a combination of all six of these energies and so to ask "how do we know what energy it has" in general makes little sense. However, for the purposes of illustrating points in physics, we would say that an object that is moving has Kinetic Energy, an object above the surface of the Earth has gravitation potential energy, and a stretched rubber band has elastic potential energy.
As far as how these energies relate to forces, on must be cautions. In order to cause any change in an object there must be a change in energy. Many times this corresponds to doing work which requires applying a force over a distance. So, to store energy in an elastic band one must apply a force and stretch the band a distance. This does work to the elastic band which is stored in in the stretched band as elastic potential energy. Releasing the band allows the potential energy to be converted to some other form as perhaps kinetic energy in flinging the band across the room at the student in front of you. Or the stored energy can be recaptured to apply a force over a distance and do work.