Please see the documentation for Subscript:

http://reference.wolfram.com/language/ref/Subscript.html

Subscript is mostly useful for creating formatted output for reading. I would only suggest using Subscripts in code to experienced Mathematica programmers. Subscripted variables are full expressions and this creates confusion with newer programmers.

With[{xn = Subscript[x, n]}, 
 Subscript[x, n + 1] == 2 f[xn] f'[xn]/(2 xn^2 - f[xn] f''[xn])]

I'm not sure I understand your follow-up. I mean Wolfram|Alpha isn't for programming really. You kinda try things and if they work, then they work. Are you looking to use Subscripted variables with it or have it output formatted math formula? My advice is to just try it.