You can change the way a field is displayed with \DeclareFieldFormat.
So all you have to do is redefine \DeclareFieldFormat for the relevant fields.
There are a few caveats, though,
Not all 'fields' are fields. biblatex knows fields, lists and name lists. These three types use different \Declare...Format directives. So you need to know the type of your field
You need to know the original definition if you don't want to override it completely. I'm assuming here that you still want italics and quotation marks as usual, only the colour should change.
- Even though it is possible to patch the field format with
xpatch's \xpretofieldformat, you need to know if any types get a special treatment. Because you can only patch the general or the type-specific format, but never both at the same time.
For the standard styles most formatting directives can be found in biblatex.def.
For fields this should be as easy as searching for the field, copying the \DeclareFieldFormat and adding in a \color{...} command in the definition. Don't forget that there might be several type-sepcific \DeclareFieldFormats for the same field (in the standard styles you should find them next to each other).
For lists you would do a similar thing, but you would search for \DeclareListFormat. (See publisher below.)
Names are more complicated. You first have to find out which name format the name you want to colour uses. author uses the format sortname in style=authoryear. And sortname is defined as family-given/given-family. So we copy the definition of family-given/given-family, call it coloured:family-given/given-family, add \colour{...} and tell sortname to be coloured:family-given/given-family from now on.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=authoryear, backend=biber]{biblatex}
\addbibresource{biblatex-examples.bib}
\usepackage[svgnames]{xcolor}
\DeclareFieldFormat{volume}{\color{DarkBlue}\bibstring{volume}~#1}% volume of a book
\DeclareFieldFormat[article,periodical]{volume}{\color{DarkBlue}#1}% volume of a journal
\DeclareFieldFormat{pages}{\color{Turquoise}\mkpageprefix[bookpagination]{#1}}
\DeclareFieldFormat{url}{\mkbibacro{URL}\addcolon\space\color{Brown}\url{#1}}
\DeclareFieldFormat{title}{\color{Red}\mkbibemph{#1}}
\DeclareFieldFormat
[article,inbook,incollection,inproceedings,patent,thesis,unpublished]
{title}{\color{Red}\mkbibquote{#1\isdot}}
\DeclareFieldFormat
[suppbook,suppcollection,suppperiodical]
{title}{\color{Red}#1}
\DeclareFieldFormat{isbn}{\mkbibacro{ISBN}\addcolon\space \color{Yellow}#1}
\DeclareFieldFormat{booktitle}{\color{Pink}\mkbibemph{#1}}
\DeclareListFormat{publisher}{%
\color{Orange}%
\usebibmacro{list:delim}{#1}%
#1\isdot
\usebibmacro{list:andothers}}
\DeclareNameFormat{coloured:family-given/given-family}{%
\color{Grey}%
\ifnumequal{\value{listcount}}{1}
{\ifgiveninits
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}%
\ifboolexpe{%
test {\ifdefvoid\namepartgiven}
and
test {\ifdefvoid\namepartprefix}}
{}
{\usebibmacro{name:revsdelim}}}
{\ifgiveninits
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}}%
\usebibmacro{name:andothers}}
\DeclareNameAlias{sortname}{coloured:family-given/given-family}
\begin{document}
\cite{sigfridsson,vizedom:related,westfahl:space,worman,geer,nussbaum,ctan}
\printbibliography
\end{document}

You can use the Biber option --validate-datamodel when compiling to help you check if your entries conform to the data model.
[DK]in the bibliography entry[DK] Donald .... I'm usingbiber. – Sigur Mar 16 '19 at 00:03labelnumberwidth(fornumericstyles) orlabelalphawidth(foralphabeticstyles). If that does not work, please ask a new question with an MWE that shows which style you use. – moewe Mar 16 '19 at 07:14\DeclareFieldFormat{labelalphawidth}{\textcolor{red}{\bibleftbracket#1\bibrightbracket}}I got all labels in red. Now, I'd like to do this for some, not all of them. Regards. – Sigur Mar 16 '19 at 12:00biblatexwhich labels to turn red? You could use\ifkeyword,\ifentrytypeor similar tests. If that does not give you what you want, please ask a new question with detailed specification of what you are after and an MWE. – moewe Mar 16 '19 at 12:09bibfiles, and citations from one should be printed in red. So, you say to insert some keyword on those bib items? Then, I embrace the filed format command? – Sigur Mar 16 '19 at 12:11.bibfile (https://tex.stackexchange.com/q/35279/35864) and then you would say\DeclareFieldFormat{labelalphawidth}{% \ifkeyword{fileone} {\textcolor{red}{\mkbibbrackets{#1}}} {\ifkeyword{filetwo} {\textcolor{red}{\mkbibbrackets{#1}}} {\mkbibbrackets{#1}}}}or something like that. – moewe Mar 16 '19 at 12:15