Once installed, Elpy will automatically provide code completion, syntax error highlighting and function signature (in the modeline) for python files.
Elpy has quite a lot of keybindings, but the following ones should be enough to get you started:
C-c C-c evaluates the current script (or region if something is selected) in an interactive python shell. The python shell is automatically displayed aside of your script (if not already there).
C-RET evaluates the current statement (current line plus the following nested lines).
C-c C-z switches between your script and the interactive shell.
C-c C-d displays documentation for the thing under cursor (function or module). The documentation will pop in a different buffer, that can be closed with q.
Elpy offers a lot of features, including code navigation, debugging, testing, refactoring, profiling and support for virtual environments. Feel free to explore the documentation, everything is there !