There's two modes: command mode, and insert mode. Command mode is where you do things that would normally be accessed via cursor, arrow keys or a menu, and insert mode is where you type letters and they appear on the screen and you can use the arrow keys like you're used to. When you open vim, you start in command mode.
This should get you to about a nano level of proficiency.
open foo | vim foo
save file | :w
quit file | :q
Command mode | [ESC]
Move cursor left, right, up, down | h l
Insert here | i
Insert new line below | o
Delete char under cursor | xHere's a nice cheat sheet for further use.