The easiest way to learn to use SnapPy is to watch the screencasts available on YouTube:
An hour-long demo Practical computation with hyperbolic 3-manifolds, recorded at the Thurston Memorial Conference.
The SnapPy 2.0 new feature demo.
Notes, problem sheets, and references from the LMS-CMI Research School in Warwick in 2017.
Another hour-long demo Practical computations with hyperbolic 3-manifolds given at ICERM in 2019.
The key thing to remember when using the SnapPy command shell window is that you can explore objects using introspection and tab-completion:
In : Manifold? <hit return-key> ...instructions for creating a manifold...
So now we create a manifold:
In : M = Manifold("m004")
But what can we do with it?
In : M.<hit tab-key> ...list of methods...
What does the “cover” method do?
In : M.cover? <hit return-key> ...description of cover method..