ayu is still in development and a lot of things need to be covered. Theme works only if VIM supports termguicolors option. This is true for Neovim and VIM from 7.4.1799.

Plug 'ayu-theme/ayu-vim' " or other package manager
"...
set termguicolors     " enable true colors support
let ayucolor="light"  " for light version of theme
let ayucolor="mirage" " for mirage version of theme
let ayucolor="dark"   " for dark version of theme
colorscheme ayu

For now In /term you can find color schemes for iTerm. More to come.

To get indent line like in the screenshot install https://github.com/Yggdroot/indentLine with my version of Roboto Mono for Powerline from this repo and add this config. In this Roboto Mono version added powerline glyphs and increased line-height of the font itself.

" IndentLine {{
let g:indentLine_char = ''
let g:indentLine_first_char = ''
let g:indentLine_showFirstIndentLevel = 1
let g:indentLine_setColors = 0
" }}