The easiest way is adding them with \cventry, which takes one optional argument (the vertical space following the entry) and six arguments, out of which number 3-6 can be {}, in which case they won't be typeset.
I show a basic application first, and then a customized macro \cvconference, which is basically \cventry (as defined in moderncvstyleclassic.sty) with a few random font changes, which you can adapt to your liking. You could do the same thing for mandates.
As a matter of fact, moderncv is a good way of starting to look into packages and finding out how things are defined. If you feel like you have a good basic understanding of LaTeX, take a look into the .sty files of moderncv. You don't have to understand everything, just try to find out what is defined where, copy a definition you want to play around with to your .tex document, and play around with it, see what happens.
\documentclass{moderncv}
\moderncvstyle{casual}
\firstname{John}
\familyname{Doe}
% copied and adapted from moderncvstyleclassic.sty
% customizations are made before the elements #2 - #7
\newcommand*{\cvconference}[7][.25em]{%
\cvitem[#1]{\color{blue}#2}{%
{\scshape#3}%
\ifthenelse{\equal{#4}{}}{}{, {\itshape#4}}%
\ifthenelse{\equal{#5}{}}{}{, {\color{red}#5}}%
\ifthenelse{\equal{#6}{}}{}{, {\sffamily#6}}%
.\strut%
\ifx&%
\else{\newline{}\begin{minipage}[t]{\linewidth}\small% next line: customization
\fontfamily{pzc}\selectfont% The percent signs are necessary!
#7\end{minipage}}\fi}}
\begin{document}
\section{Conferences}
\cventry{2012}{\TeX.sx symposium}{Additional \texttt{moderncv} types}{The Internet}{Another Category}{And here are some details about that.} % arguments 3 to 6 can be left empty
\cventry{Date}{Name of the congress}{Title of my presentation}{Place (city, country)}{Etc.}{Description}
\cvconference{2012}{\TeX.sx symposium}{Additional \texttt{moderncv} types}{The Internet}{Another Category}{And here are some details about that.} % arguments 3 to 6 can be left empty
\cvconference{Date}{Name of the congress}{Title of my presentation}{Place (city, country)}{Etc.}{Description}
\section{Mandates}
\cventry{Oct.~2012}{Peter Pan, Abe Lincoln}{Donald Knuth}{Willy Wonka's Chocolate Factory}{The Golden Ticket}{Well, let me tell you a little story ...}
\cventry{Date}{Names of the writers (me and colleagues)}{Name of the person who gives the mandate}{Name of the company}{Title of the mandate}{Small description of the mandate}
\end{document}
