Simple school style report headers

The solution below uses fancyhdr and puts the content you described in a minipage.

Following @Seamus' comment, I have increased the headheight using the geometry package.

\documentclass{article}
\usepackage[showframe=true,headheight=1cm]{geometry}
\usepackage{fancyhdr} % for headers and footers
\usepackage{lipsum}   % for dummy text

\begin{document}

% headers
\fancyhead[L]{}
\fancyhead[C]{}
\fancyhead[R]{%
\begin{minipage}{3cm}
 \raggedleft 
 Hughes\\
 Math 251: Calc\\
 MW 9am-11.30am
\end{minipage}}
\renewcommand{\headrulewidth}{0pt}

% footers
\fancyfoot[L]{left foot}
\fancyfoot[C]{center foot}
\fancyfoot[R]{right foot}

% need to specify the pagestyle as fancy
\pagestyle{fancy}
\lipsum

% if you want a non-fancy pages from this point use ... 
\pagestyle{plain}
\lipsum

\end{document}

If you only want the information to appear in the header on the first page it might be appropriate to use

\pagestyle{plain}
\thispagestyle{fancy}

at the beginning of your document.

The titlesec package also offers a set of commands for one-step headline and footline settings (see Section 5. Page Styles of the package documentation). Here's a little example, placing the required information (on every page) flushed to the right margin, and the page number in the center of the footer:

\documentclass{article}
\usepackage[pagestyles]{titlesec} 
\usepackage{lipsum} % just to generate text for the example

\addtolength\headheight{6pt}

\newpagestyle{mystyle}{
  \sethead{}{}{\begin{minipage}{3.5cm}
                                 \raggedleft 
                                 The Professor\\
                                 The Class\\
                                 The Time
                               \end{minipage}}
  \setfoot{}{\thepage}{}
}

\pagestyle{mystyle}

\begin{document}

\lipsum[1-14]

\end{document}