Ensure there's a syntax directory in the personal vim directory.

 mkdir -p ~/.vim/syntax

Download the markdown syntax file and put it in this directory (e.g. markdown.vim).

Affect the markdown filetype to *.mdwn files and avoid long lines (in ~/.vimrc).

 " Help autodetection
 augroup filetypedetect
     au! BufRead,BufNewFile *.mdwn setfiletype markdown
 augroup END

 " Limit the line length for this mode
 autocmd FileType markdown set tw=80

Enjoy.