The advice above is accurate it is just missing something.
If you go to view the post page that you would like to remove the date/author from in your web browser. Using what ever functionality the browser has to look at the raw html code search the code for the author name .
you should find something that looks similar to
<h2 class="post-meta"> by <a href="http://www.BlaaBlaaBlaa.com/author/jason/" title="Posts by Jason" rel="author">Jason</a>
<a class="date-anchor" href="http://www.BlaaBlaaBlaa.com
now obviously if your name is not Jason then the title Posts by XXX will say something different :)
The important thing to see here is the class entry what ever that is in your page code. Here it is "post-meta" also note the class entry "date-anchor"
if you add to your style.css the lines
that class will not display any more (unless it is overriden by a later css entry). so for me the entry
removed the date and author
and looking around a bit more in the code the entry
hides the category entries before the title.
now if you wanted to remove only the date then the entry
would do that.
The class names are not necessarily set in the WordPress implementation but depend on the mood and imagination of the theme creator on the day its css files are written. [This last allegation may be unsubstantiated*]
*the allegation about implementation not imagination, I'm sure programmers have imagination, I like to think i do.