How to make a traditional division

One option would be to use the xlop package:

\documentclass{report}
\usepackage{xlop}

\begin{document} 

\opidiv{25}{7}\qquad\opdiv{25}{7}

\end{document}

Manually, you can use an array:

\documentclass{article}

\newcommand\myrule[1]{\multicolumn{1}{| l}{#1}}

\begin{document}

\[
\begin{array}{rl}
478 & \myrule{7} \\
\cline{2-2}
58 & 68 \\
2
\end{array}
\]

\end{document}

If you are only interested in the dividend, divisor, quotient and remainder, you can define a two-argument command (quotient and remainder can be automatically calculated) along the lines of

\documentclass{article}
\usepackage{intcalc}


\newcommand\mydiv[2]{%
\ifnum#2>0
\[
\renewcommand\arraystretch{1.2}
\begin{array}{@{}r | l}
#1 & #2 \\
\cline{2-2}
\multicolumn{1}{r}{\intcalcMod{#1}{#2}} 
& 
\ifnum#1>0\relax
  \intcalcDiv{#1}{#2}
\else
  \number\numexpr\intcalcDiv{#1}{#2}-1\relax
\fi
\end{array}
\]
\else
\GenericWarning{}{Division Warning: "Please provide a positive integer as divisor"}
\fi
}


\begin{document}

\mydiv{478}{7}

\end{document}

For the simple diagrams you can do in this way:

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\division}{smm}
 {
  \IfBooleanTF{#1}
   { \fabricio_division_inline:nn { #2 } { #3 } }
   { \fabricio_division:nn { #2 } { #3 } }
 }

\cs_new:Npn \fabricio_division_inline:nn #1 #2
 {
  #1=#2\cdot\int_div_truncate:nn { #1 } { #2 }
     + \int_mod:nn { #1 } { #2 }
 }
\cs_new_protected:Npn \fabricio_division:nn #1 #2
 {
  \begin{array}{r | l}
  #1 & #2 \\
  \cline{2-2}
  \multicolumn{1}{r}{\int_mod:nn { #1 } { #2 }} &
    \int_div_truncate:nn { #1 } { #2 }
  \end{array}
 }
\ExplSyntaxOff

\begin{document}
\[
\division*{1234}{42}
\qquad
\division{1234}{42}
\]
\end{document}

The *-form just prints the division in the form a=bq+r.