coordinates of phase space

Hi,
I am u little confused about general coordinates at all. I don't know
functions of what are they.
For exhample on Hamiltons phase space there are $p$ and
$q$. Are thesse function of time?
I've seen that $\frac{\partial q }{\partial t}=0$ but total derivation
is not . .. what is difference if $q$ is function jus $t$?

Thanks a lot!.