This list of commands should give one a good start into the wonderful world of Vim.
h -> left
j -> down
k -> up
l -> right
w -> next word beginning
b -> previous word beginning
e -> next word ending
g -> begin of document
G -> end of Document
nG -> move to first letter in line number
fc -> move cursor on next occourence of character c in line
tc -> move cursor on character before the next occourence of character c in line
0 -> begin of line
^ -> first letter of line
$ -> end of line
H -> first visible line
M -> middle of display
L -> last visible line
CTRL-U -> scroll Up
CTRL-D -> scroll Down
Most of those commands can be combined with numbers like the G command
i -> insert before cursor
a -> append after cursor (try something like a3!)
I -> insert at begin of line
A -> append to end of line
o -> add line under current line and switch to insert mode
O -> add line above current line and switch to insert mode
dd -> delete current line (d5d deletes 5 lines)
x -> delete character (4x deletes 4 characters)
yy -> yanks/copies current line
p -> insert last deleted/yanked text (put)
cw -> change word
ci( -> change everything inside () (works with [ too)
rc -> replace character with c (rT replaces current char with T)
J -> joins current and next line
. -> repeat commands (try to experiment with that a bit, it's nice)
u -> undo
CTRL-R -> redo
/text -> go to next occourence of text