Setting Emacs to Split Buffers Side-by-Side

(setq split-height-threshold nil)
(setq split-width-threshold 0)

GNU Emacs Lisp Reference Manual: Choosing Window Options

Two solutions here, use any one you like:

A: Vertically(left/right) by default:

(setq split-height-threshold nil)
(setq split-width-threshold 0)

B: Automatically split window vertically(left/right) if current window is wide enough

(defun display-new-buffer (buffer force-other-window)
  "If BUFFER is visible, select it.
If it's not visible and there's only one window, split the
current window and select BUFFER in the new window. If the
current window (before the split) is more than 100 columns wide,
split horizontally(left/right), else split vertically(up/down).
If the current buffer contains more than one window, select
BUFFER in the least recently used window.
This function returns the window which holds BUFFER.
FORCE-OTHER-WINDOW is ignored."
  (or (get-buffer-window buffer)
    (if (one-window-p)
        (let ((new-win
               (if (> (window-width) 100)
                   (split-window-horizontally)
                 (split-window-vertically))))
          (set-window-buffer new-win buffer)
          new-win)
      (let ((new-win (get-lru-window)))
        (set-window-buffer new-win buffer)
        new-win))))
;; use display-buffer-alist instead of display-buffer-function if the following line won't work
(setq display-buffer-function 'display-new-buffer)

Put any one in you .emacs/init.el file. You can change the "100" to the value you like, depending on you screen.

If you got two windows in one frame, and you want to change the layout from vertical to horizontal or vice verse, here is a solution:

(defun toggle-window-split ()
  (interactive)
    (if (= (count-windows) 2)
      (let* ((this-win-buffer (window-buffer))
            (next-win-buffer (window-buffer (next-window)))
            (this-win-edges (window-edges (selected-window)))
            (next-win-edges (window-edges (next-window)))
            (this-win-2nd
             (not (and (<= (car this-win-edges)
                        (car next-win-edges))
                    (<= (cadr this-win-edges)
                        (cadr next-win-edges)))))
         (splitter
          (if (= (car this-win-edges)
                 (car (window-edges (next-window))))
              'split-window-horizontally
            'split-window-vertically)))
    (delete-other-windows)
    (let ((first-win (selected-window)))
      (funcall splitter)
      (if this-win-2nd (other-window 1))
      (set-window-buffer (selected-window) this-win-buffer)
      (set-window-buffer (next-window) next-win-buffer)
      (select-window first-win)
      (if this-win-2nd (other-window 1))))))
;; C-x 4 t 'toggle-window-split
(define-key ctl-x-4-map "t" 'toggle-window-split)

Put it in your .emacs/init.el file, Use C-x 4 t to toggle the layout of your windows.

(setq split-height-threshold 0) (setq split-width-threshold 0)

is what i had to use to get the desired behaviour (no horizontal splitting)