Creating unnumbered chapters/sections (plus adding them to the ToC and/or header)

To get unnumbered chapters, parts, sections, subsections, etc, you just affix a * (asterisk) to the respective sectioning command; hence, you'd type something like

\section*{Acknowledgments} 

or

\chapter*{Introduction}

Exactly which sectioning command you ought to use will depend importantly on aspects of the document that you haven't told us about. E.g., should the respective parts begin on a page of their own, and how prominent do you want the caption of the sectioning command to be?

Note that unnumbered parts, chapters, sections, etc are not included automatically in the table of contents (ToC). In case you need some (or all) of them to be included, you should insert an \addcontentsline instruction after each such sectioning command. For example, you'd type:

\chapter*{Foreword} 
\addcontentsline{toc}{chapter}{Foreword}

The second argument of the \addcontentsline instruction -- here, chapter -- instructs LaTeX to typeset the entry in a given style, here, "chapter style".

The following MWE

\documentclass{report}
\begin{document}
\tableofcontents
\chapter*{Acknowledgments}
\addcontentsline{toc}{chapter}{Acknowledgments}
\chapter*{Introduction}
\addcontentsline{toc}{chapter}{Introduction}
\chapter{Experiments}
\chapter{Conclusion}
\end{document}

generates this ToC:

Besides adding unnumbered chapters/sections to the ToC, you may also want to ensure that they are correctly displayed in the header/footer. In the report and book class this may be done by writing, e.g.,

\chapter*{Introduction}
\markboth{Introduction}{Introduction}

for unnumbered chapters (the second argument of \markboth controls "right" [odd] pages in twoside documents; it may also be left empty) and

\section*{Introduction}
\markright{Introduction}

for unnumbered sections. (Should you have enabled headers in the article class, use \markboth in conjunction with \section* and \markright in conjunction with \subsection*.)

Note that the above code snippets will produce non-capitalized names in the header; should you want to capitalize them (as for numbered chapters in the standard classes), replace Introduction with \MakeUppercase{Introduction}.

Addendum: Both Mico's and my answer refer to the standard document classes (article, book, report). The answers should work for most other classes; however, some classes may offer easier solutions. E.g., with the KOMA-Script classes you may simply use the commands \addchap/\addsec to create unnumbered chapters/sections that will be displayed in the ToC and the header.

A little package on github that might never hit CTAN can be of help here.

It takes care of the entries and the headings automatically.

\documentclass{book}
\usepackage{blindtext}
\usepackage[
    %   indentunnumbered
]{unnumberedtotoc} %get it from https://github.com/johannesbottcher/unnumberedtotoc
\usepackage{hyperref}

\begin{document}
\tableofcontents

\addchap{unnumbered chapter with toc and head}
\blindtext[10]

\addchap[title for toc and head]{chapter title}
\blindtext[10]
\addsec*{starred addsec}
\blindtext[10]
\addsec{regular addsec}
\blindtext[10]
\addsec*{starred addsec}
\blindtext[10]
\chapter{usual chapter}
\blindtext[10]
\chapter*{look at the header}
\blindtext[10]
\addchap*{really nothing, header cleared}
\blindtext[10]
\end{document}