How to automatically close NERDTree after a file has been opened?

Try :help nerdtreequitonopen.

Add the following to your .vimrc

let NERDTreeQuitOnOpen=1

Add this line to your .vimrc:

let NERDTreeQuitOnOpen='Value'

and Values :

 Value  | NERDTree Window Behavior
 -------+-------------------------------------------------------
 0      | No change
 1      | Closes after opening a file
 2      | Closes the bookmark table after opening a bookmark
 3(1+2) | Same as both 1 and 2