Following instructions from Chinese typing on mac , I can type Chinese in TexShop, the characters shows properly in PDF file.
What I did is replacing
\documentclass[10pt]{article}
with
% !TEX program = XeLaTeX
% !TEX encoding = UTF-8 Unicode
\documentclass[UTF8,nofonts,10pt]{ctexart}
\setCJKmainfont[BoldFont=FandolSong-Bold.otf,ItalicFont=FandolKai-Regular.otf]{FandolSong-Regular.otf}
\setCJKsansfont[BoldFont=FandolHei-Bold.otf]{FandolHei-Regular.otf}
\setCJKmonofont{FandolFang-Regular.otf}
However, after changing the tex file header, the line spacing becomes bigger.
Before

After

Edit according to request from comments:
The part generating the paragraph is like this:
\noindent Let $E/F$ be a field extension, $\alpha \in E$. The {\bf minimal polynomial} of $\alpha$ is the monic polynomial of least degree among all polynomials in $F[x]$ having $\alpha$ as a root; it exists when $\alpha$ is algebraic over $F$, that is, when $f(\alpha) = 0$ for some non-zero polynomial $f(x) \in F[x]$. 最小多项式
The whole tex file is as below (I copied the header from somewhere else, not really understand every line)
% !TEX program = XeLaTeX
% !TEX encoding = UTF-8 Unicode
\documentclass[UTF8,nofonts,10pt]{ctexart}
\setCJKmainfont[BoldFont=FandolSong-Bold.otf,ItalicFont=FandolKai-Regular.otf]{FandolSong-Regular.otf}
\setCJKsansfont[BoldFont=FandolHei-Bold.otf]{FandolHei-Regular.otf}
\setCJKmonofont{FandolFang-Regular.otf}
\usepackage{amsfonts,amssymb,amsmath,amsthm,epsfig,latexsym}
\newcommand{\nc}{\newcommand}
\def\nr{\par \noindent}
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{definition}{Definition}
\newtheorem{prop}{Proposition}
\newtheorem{corollary}{Corollary}
\newtheorem{remark}{Remark}
% This is FULLPAGE.STY by H.Partl, Version 2 as of 15 Dec 1988.
% Document Style Option to fill the paper just like Plain TeX.
\typeout{Style Option FULLPAGE Version 2 as of 15 Dec 1988}
\topmargin 0pt \advance \topmargin by -\headheight \advance
\topmargin by -\headsep
\textheight 8.9in
\oddsidemargin 0pt \evensidemargin \oddsidemargin \marginparwidth
0.5in
\textwidth 6.5in
% For users of A4 paper: The above values are suited for american 8.5x11in
% paper. If your output driver performs a conversion for A4 paper, keep
% those values. If your output driver conforms to the TeX standard (1in/1in),
% then you should add the following commands to center the text on A4 paper:
% \advance\hoffset by -3mm % A4 is narrower.
% \advance\voffset by 8mm % A4 is taller.
\begin{document}
\noindent Let $E/F$ be a field extension, $\alpha \in E$. The {\bf minimal polynomial} of $\alpha$ is the monic polynomial of least degree among all polynomials in $F[x]$ having $\alpha$ as a root; it exists when $\alpha$ is algebraic over $F$, that is, when $f(\alpha) = 0$ for some non-zero polynomial $f(x) \in F[x]$. 最小多项式
\end{document}
% !TEX encoding = UTF-8 Unicodeon the same line as% !TEX program = XeLaTeX, which probably made the former comment ineffective. – Franck Pastor Mar 07 '15 at 08:15ctexbundle changes the document layout a lot, including the line spacing. You can use\linespread{1}to make the text single spaced. – Leo Liu Mar 07 '15 at 08:34xeCJKand set the fonts. See also http://tex.stackexchange.com/a/17637/2674 – Leo Liu Mar 07 '15 at 09:27