Would appreciate some advice on child selectors please.

I have a navbar, navbar-inner and want to influence the list w/in it.
tried
navbar-inner>.ul { height:###;}
tried
navbar ul { height:###;}
eventually setteled for giving the navbar an id and
#id ul { height:###;}

what is the correct way to use a child selector to influence an element?
while at it can someone please explain or point me to a link for the diff between
.class .class {} (or id, w/ a space after the first selector)
and
.class.class {} (or id, w/out a space after the first selector)

thank you
d