What is chemical free energy?
Chemical Free Energy or Gibbs Free Energy is best understood as potential energy for reactions.

If I have a lot of Gibbs Free Energy, then I have a lot of potential energy.
Kind of like if I were on top of a hill, it's very easy for me to roll down that hill.

Often what's talked about in books is dG or the change in Gibbs Free Energy. If we think of it is simply being on top of a hill (High Gibbs Free Energy/Potential Energy) G(initial)
 going to the bottom of the hill (Low Gibbs Free Energy/Potential Energy) G(final)

Then the change in Gibbs Free Energy will be negative for something spontaneous (like the rolling down a hill example). 
Change is always calculated as: change = final - initial

Gibbs Free Energy is used in the same was as potential energy. But instead of translating to kinetic energy, it translates to Enthalpy (heat) and/or Electrochemical Energy (being able to move electrons). Both Enthalpy and Electrochemical Energy can then be converted to mechanical work.

The way to think about it is not so much that you can use Gibbs Free Energy, but rather it's just the innate property of whatever situation you're working with. Molecules have a tendency to be reduced or oxidized under different conditions, the Gibbs Free Energy just tells you which way is spontaneous.

dG = dH - TdS

This gets kind of complicated, since dG is affected by many factors, but it gives you an idea, that the Change in Gibbs Free Energy can become positive or negative under different conditions.

Keep in mind that Gibbs Free Energy isn't a real thing, but rather a concept that helps explain why things happen.
 Why do gases expand?
 I don't know, but the universe has a tendency to do this. So we say that it is spontaneous, just like how we would say things roll down a hill because of gravity.
 What's gravity?
 It's our way of explaining why things roll down hills. :p

I hope that helps a little bit.