You are actually pretty close. If you look at moewe's canonical answer on the topic you can get a better grasp on the possibilities and requirements of creating a new entrytype.
Still, to get your new fields typeset in the bibliography, you are critically missing a driver for you manuscript entrytype. I'm not sure the format you are looking for, but this serves as an example:
\DeclareBibliographyDriver{manuscript}{%
\usebibmacro{begentry}%
\printfield{library}%
\setunit{\addcomma\space}%
\printlist{location}%
\newunit\newblock
\printfield{title}%
\setunit{\addcomma\space}%
\printfield{datation}%
\usebibmacro{finentry}%
}
I've also removed title and library from your .dbx file, as they are already defined by default. You should still add them to your \DeclareDatamodelEntryfields[manuscript]{... as you do. Also, note that setting both citestyle and bibstyle to verbose is equivalent to the more direct style=verbose.
In full:
\documentclass{article}
\usepackage[datamodel=manuscript,style=verbose]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{manuscript.dbx}
\DeclareDatamodelEntrytypes{manuscript}
\DeclareDatamodelFields[type=field, datatype=literal]{datation}
\DeclareDatamodelEntryfields[manuscript]{
title,
library,
location,
datation}
\end{filecontents}
\begin{filecontents}{manuscript.bib}
@manuscript{P1470,
library = {BNF},
title = {A title},
location = {Paris},
datation = {\textsc{viii}\textsuperscript{e} s.},
}
\end{filecontents}
\DeclareBibliographyDriver{manuscript}{%
\usebibmacro{begentry}%
\printfield{library}%
\setunit{\addcomma\space}%
\printlist{location}%
\newunit\newblock
\printfield{title}%
\setunit{\addcomma\space}%
\printfield{datation}%
\usebibmacro{finentry}%
}
\DeclareFieldFormat[manuscript]{title}{\mkbibquote{#1\isdot}}
\addbibresource{manuscript.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

You can, and should, examine closer moewe's linked answer, particularly the formatting directives. Also, you can redefine your bibdriver to the order of fields and punctuation of your liking.
biblatex's jargon needs some getting used to, but once you grasp it you'll see it has a logic. I hope it has been enough to get you started. moewe's answer, specially, is very thorough. But old time languages should be no impediment. I started myself with Basic on a TK85 (a ZX81 clone) with K7 tape memory and all! :) – gusbrs Dec 17 '18 at 11:12