pyLyapunov contains just one function so far, computeLE. It computes the Lyapunov exponents for a set of ODEs.
See the example files for guidance on how to run the calculation. Importantly, you need to define the ODEs (f) and their Jacobian (fjac) in a separate Python module. f and fjac should be in "scipy.integrate.ode style", which means that they take their arguments in the very specific order: t, x, *p where t and x are the time and position now, and any extra parameters get passed in after t and x (not in a tuple, but as extra individual arguments). However, the parameters should be passed to computeLE in a tuple!
Once you have this, define an array of times t over which to perform the calculation; additionally, if you want to integrate out transient behavior first, then define an array of times ttrans and pass it to computeLE. Finally, decide on an initial position for the calculation (or the initial position for the integration of the transient behavior, if ttrans is specified).
computeLE returns an array of exponents at all times t. The last one should, in some sense, be the most accurate, since at each time the exponents are averaged up to that time point.