To search a file, type / (search forwards) or ? (search backwards) and enter the word.

Normally, Vim will check for upper and lower letters. But you can set two different options in your configuration file (~/.vimrc or similar):

set ignorecase

or

set smartcase

Examples:

      pattern	'ignorecase'  'smartcase'	matches ~
	foo	  off		-		foo
	foo	  on		-		foo Foo FOO
	Foo	  on		off		foo Foo FOO
	Foo	  on		on		    Foo
	\cfoo	  -		-		foo Foo FOO
	foo\C	  -		-		foo

Other options:

:set incsearch - show match as search proceeds
:set hlsearch  - search highlighting

Vim will jump to the first match. Hit Enter if you’re finished with typing. Then you can circle through all matches with n (forwards) or N (backwards).

You can also search for the current word. Press * and Vim will search forwards. With # Vim will search backwards. Both commands will do an exact search. If your cursor is on the word for, it won’t match forwards. You can fuzzy search with g* or g#.

Hit / or ? and arrow keys for your search history.

Further Reading