For example:
\documentclass{article}
\usepackage{fancyhdr}
\usepackage{blindtext}
\pagestyle{fancy}
\fancyhf{}
\fancyhead[L]{\leftmark} % displays the section (1. SECTION NAME)
\fancyhead[R]{\rightmark} % displays the subsection (1.1 SUBSECTION NAME)
\fancyfoot[R]{\thesubsubsection \subsubsectionname} % doesn't work
% would like the above line to produce (1.1.1 Subsubsection name), for example.
\begin{document}
\blinddocument
\end{document}
Updated example that exhibits the problems I'm having:
\documentclass{article}
\usepackage{tabu,kantlipsum}
\usepackage{longtable}
\usepackage{titleps}
\usepackage{datetime}
\usepackage[left=1cm, right=1cm, bottom=1in]{geometry}
\usepackage[bookmarks]{hyperref}
\usepackage[auth-sc,affil-it]{authblk}
\title{A Title}
\author[1]{An Author\thanks{\texttt{email@email}}}
\affil{Department of LateX}
\date{Dated: \today}
\newpagestyle{mypage}{%
\headrule
\sethead{ \thesection\quad \sectiontitle }{ \thesubsection\quad \subsectiontitle }{ \thesubsubsection\quad \subsubsectiontitle }
\setfoot{Generated: \today \hspace{1ex} \currenttime}{\thepage}{Some other footer text}
\footrule
}
%\settitlemarks{section, subsection, subsubsection} % cannot do this!!
\settitlemarks{section,subsection,subsubsection} % must NOT put spaces in this!
\pagestyle{mypage}
\begin{document}
\maketitle
\tableofcontents
\pagebreak
\section{Section one}
\kant[1-4]
\subsection{Subsection one}
\kant[5-10]
\subsubsection{Subsubsection one}
\kant[11-20]
\end{document}

\begin{document}yet, let alone included any subsubsections!' which is likely rather unhelpful. – cfr Apr 03 '15 at 22:13fancyhdr. However, I may not have understood. – cfr Apr 03 '15 at 22:23