What is the simplest way to put some text at the beginning of a line and to put some text at the center of the same line?

For example:

\documentclass{article}
\begin{document}

\hrule % show line width

\noindent\rlap{(H)}\hfill some text\hfill\null\par

\hrule

\end{document}

\noindent starts a new paragraph without indentation of the first line. \rlap prints its argument to the right. The middle text is centered by wrapping it in \hfill...\hfill. The \null at the end of the paragraph (\par) prevents that TeX removes the previous \hfill (TeX removes the last horizontal space at the end of the paragraph).

The \hfill at the right side can be replaced by the automatically inserted \parfillskip:

\noindent\rlap{(H)}\hfill some text{\setlength{\parfillskip}{\fill}\par}

Here's a fully LaTeX compliant solution.

\documentclass{article}
\usepackage{showframe} % just for the example

\newcommand{\lcrline}[3]{%
  \par % we want to be on a line by itself
  \noindent % no indent
  \makebox[\linewidth][s]{% spread to the line width
    \makebox[0pt][l]{#1}% text at left
    \hfill
    \makebox[0pt][c]{#2}% text at center
    \hfill
    \makebox[0pt][r]{#3}% text at right
  }%
  \par
}

\begin{document}

\lcrline{(H)}{some text}{}

\bigskip

\lcrline{Left}{Longer text in the middle}{Right}

\end{document}

Well, also

\def\lcrline#1#2#3{\par\hbox to \linewidth{\rlap{#1}\hss#2\hss\llap{#3}}

would work essentially the same. Why not using this? Because the above solution only uses documented commands in the LaTeX manual and, in case of a new version is released that breaks the macro above, you can hold it against the maintainers; the other one (similar in spirit to other answer to the present question) would be rejected with “we're responsible only for the documented features”.

An extended version that will warn in case there's overlap.

\documentclass{article}
\usepackage{showframe} % just for the example

\newcommand{\lcrline}[3]{%
  \par % we want to be on a line by itself
  %%% check for no overlapping
  \checklcrlineoverlap{#1}{#2}{#3}
  \noindent % no indent
  \makebox[\linewidth][s]{% spread to the line width
    \makebox[0pt][l]{#1}% text at left
    \hfill
    \makebox[0pt][c]{#2}% text at center
    \hfill
    \makebox[0pt][r]{#3}% text at right
  }%
  \par
}
\makeatletter
\newcommand\checklcrlineoverlap[3]{%
  \@tempswafalse
  \settowidth\@tempdima{#1}%
  \settowidth\@tempdimb{#2}%
  \ifdim\dimexpr\@tempdima+0.5\@tempdimb>.5\linewidth
    \@tempswatrue
  \fi
  \settowidth\@tempdima{#3}%
  \settowidth\@tempdimb{#2}%
  \ifdim\dimexpr\@tempdima+0.5\@tempdimb>.5\linewidth
    \@tempswatrue
  \fi
  \if@tempswa
    \@latex@warning{Overlap for \protect\lcrline}%
  \fi
}
\makeatother

\begin{document}

\lcrline{(H)}{some text}{}

\bigskip

\lcrline{Left}{Longer text in the middle}{Right}

\bigskip

\lcrline{Long long text at the left}{Longer longer text in the middle}{Right}

\bigskip

\lcrline{Left}{Longer longer text in the middle}{Long long text at the right}

\end{document}

The terminal and the log file would display

LaTeX Warning: Overlap for \lcrline on input line 47.

LaTeX Warning: Overlap for \lcrline on input line 51.

\usepackage{xparse}
\NewDocumentCommand\linetext{O{}mO{}}
  {\par\noindent
   \makebox[\textwidth][s]{\makebox[0pt][l]{#1}\hss\makebox[0pt][c]{#2}\hss\makebox[0pt][r]{#3}}}

And then use \linetext[left]{center}[right] where the first and third arguments are optional, hence you can write \linetext{center} or \linetext[left]{center} or \linetext{center}[right].