The code for \part and \chapter are different from the other sectional units, and like the default document classes, are contained in the class in question. So, if you're using scrreprt.cls, the following is the code that produces the layout (including font size, colour, arrangement and content):
Parts:
\def\@part[#1]#2{%
\ifnum \c@secnumdepth >-2\relax
\refstepcounter{part}\@maybeasf%
\addcontentsline{toc}{part}{\protect\numberline{\thepart}#1}%
\else
\addcontentsline{toc}{part}{#1}%
\fi
\chaptermark{}
{\centering
\interlinepenalty \@M
\normalfont
\ifnum \c@secnumdepth >-2\relax
\size@partnumber\sectfont\partformat
\par
\vskip 20\p@
\fi
\size@part\sectfont #2\par}%
\@endpart}
Chapters:
\def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne
\refstepcounter{chapter}%
\typeout{\@chapapp\space\thechapter.}%
\addcontentsline{toc}{chapter}%
{\protect\numberline{\thechapter}#1}%
\else
\addcontentsline{toc}{chapter}{#1}
\fi
\chaptermark{#1}%
\addtocontents{lof}{\protect\addvspace{10\p@}}%
\addtocontents{lot}{\protect\addvspace{10\p@}}%
\if@twocolumn
\@topnewpage[\@makechapterhead{#2}]%
\else
\@makechapterhead{#2}%
\@afterheading
\fi}
\def\@makechapterhead#1{\chapterheadstartvskip%
{\size@chapter{\sectfont
\@hangfrom{\ifnum \c@secnumdepth >\m@ne%
\chapterformat\fi}%
{\raggedsection \interlinepenalty \@M #1\par}}
\nobreak\chapterheadendvskip
}}
There is a minor difference in terms of the layout for numbered and unnumbered elements like above (for example, for \part* and \chapter*), but you can find those definitions in the source classes as well.
How would you go about changing them? Either by means of the supplied hooks provided in the KOMA-script documentation, or by updating the above definitions to your liking. For example,
Updating the font and colour for \part:
Update the macro \partformat to include colour. It's currently defined as
\newcommand*\partformat {\partname~\thepart\if@altsecnumformat.\fi}
so using
\usepackage{xcolor}% http://ctan.org/pkg/xcolor
%...
\newcommand*\partcolor{\color{blue!50}}% Part is coloured blue
\newcommand*\partformat {\partcolor\partname~\thepart\if@altsecnumformat.\fi}
The above allows you to change only \partcolor rather than reformat the entire \partformat if you want to update the colour (from one \part to another, say).
Modify the space after the chapter title:
Update the definition of \chapterheadendvskip (either via the document class option, or directly). For example,
\def\chapterheadendvskip{\vspace{50pt}}
would leave a 50pt gap between the chapter title and the start of the chapter text. This is specifically covered in the KOMA-script documentation (section 16.3. Expert Commands, p 285).
The question is very general, as such I've only given some general guidelines as to the modification of these structural units. If the class does not provide adequate control over specific elements of the layout, you'd have to modify the structural parts manually. To that end, a document class is typically considered restrictive, while (compatible) packages provide an extension or flexibility to modify things to your liking, rather than tinkering with the actual code.