Elpy has quite a lot of keybindings, but the following ones should be enough to get you started:
C-c C-c (elpy-shell-send-region-or-buffer)¶
Evaluate the current script (or region if something is selected) in an interactive python shell. The python shell is automatically displayed aside of your script.
Evaluate the current statement (current line plus the following nested lines). Useful for evaluating a function or class definition or a for loop.
C-c C-z (elpy-shell-switch-to-shell)¶
Switch between your script and the interactive shell.
C-c C-d (elpy-doc)¶
Display documentation for the thing under cursor (function or module). The documentation will pop in a different buffer, that can be closed with q.