There are several packages to configure the page header and footer. Mico has already shown an example using fancyhdr. Here one with scrlayer-scrpage:
\documentclass[12pt]{article}
\usepackage[margin=0.75in]{geometry}
\usepackage{mathptmx}
\usepackage[manualmark,pagestyleset=KOMA-Script]{scrlayer-scrpage}
\markright{Outline of Proposed Research}% set the \rightmark to "Outline of Proposed Research"
\setcounter{secnumdepth}{0}
%\pagenumbering{arabic}% default and therefore not needed
%\setlength{\parindent}{0pt}% not recommended → https://sourceforge.net/p/koma-script/wiki-en/HowTo_NoParIndent/ …
\usepackage{parskip}% … is the better solution to not indent the first line of a paragraph
%\linespread{1.0}% default and therefore not needed
\usepackage{mwe}
\begin{document}
\blinddocument
\end{document}

Note: \markright does not set the right mark of the page header, but the right part of the standard LaTeX mark originally (e.g. with page style myheadings or headings of the standard classes) supposed to be used for right (odd) pages. On single-sided documents, this mark is by default used for odd and even pages. See a LaTeX introduction or the KOMA-Script manual for more information about \markright and \markboth. See the KOMA-Script manual also for information about \markdouble, which could be used here instead of \markright and which could be useful for double-sided documents (e.g., if using class option twoside).
In your case only the two lines
\usepackage[manualmark,pagestyleset=KOMA-Script]{scrlayer-scrpage}
\markright{Outline of Proposed Research}
are needed, because it seems, that the predefined page style set KOMA-Script already shows the wanted result with a head mark in the middle of the page header and pagination in the middle of the footer. In other cases, more configuration could be needed.
Using titleps would also be possible:
\documentclass[12pt]{article}
\usepackage[margin=0.75in]{geometry}
\usepackage{mathptmx}
\usepackage{titleps}
\newpagestyle{outline}{
\sethead{}{Outline of Proposed Research}{}% header {left}{center}{right}
\setfoot{}{\thepage}{}% footer {left}{center}{right}
}
\pagestyle{outline}
\setcounter{secnumdepth}{0}
%\pagenumbering{arabic}% default and therefore not needed
%\setlength{\parindent}{0pt}% not recommended → https://sourceforge.net/p/koma-script/wiki-en/HowTo_NoParIndent/ …
\usepackage{parskip}% … is the better solution to not indent the first line of a paragraph
%\linespread{1.0}% default and therefore not needed
\usepackage{mwe}
\begin{document}
\blinddocument
\end{document}
The result is the same as shown above.
fandyhdr. – cfr Sep 20 '23 at 05:19\pagestyle{plain}also puts the page number at the bottom of the page, but no headers. Actually, you don't need any packages to create your own page style (such as\ps@myheader) – John Kormylo Sep 20 '23 at 13:01