Are HTML and CSS regular languages?
Providing a regular expression or DFA for a language and proceeding to demonstrate that it is correct for the language in question generally constitutes a pretty convincing argument for the regularity of the language. To prove a language is non-regular, you have a few options: the pumping lemma for regular languages is a classic standby, but the Myhill-Nerode theorem is pretty nifty, too (especially since you can use it to prove regularity as well as non-regularity).

Your first job should be to define what constitute valid strings in the languages $HTML$ and $CSS$. Note that most browsers will take anything you call $HTML$ and display something without error; in that sense, anything is valid $HTML$, and the language $\Sigma^*$ is trivially regular. However, I think it's safe to assume that you have something a bit more strict in mind: $HTML$ consists only of those strings that conform to some standard, which probably calls for matched tags. In this case, you should be able to prove that $HTML$ isn't regular, since you can consider the following kinds of strings (whitespace is added only for clarity and could be removed in the real string):

&lt;html&gt;
   &lt;body&gt;
      &lt;table&gt;
         &lt;tr&gt;
            &lt;td&gt;
               &lt;table&gt;
                  ...
               &lt;/table&gt;
            &lt;/td&gt;
         &lt;/tr&gt;
      &lt;/table&gt;
   &lt;/body&gt;
&lt;/html&gt;


This language, &lt;html&gt;&lt;body&gt; $($ &lt;table&gt;&lt;tr&gt;&lt;td&gt; $)^n($ &lt;/td&gt;&lt;/tr&gt;&lt;/table&gt; $)^n$`&lt;/body&gt;&lt;/html&gt;`, should be enough to get to a proof of non-regularity, provided you accept the above as valid $HTML$, and would say that a missing `&lt;/table&gt;` tag would make the resulting string invalid $HTML$, even though browsers would try to render it anyway.

For $CSS$, first figure out what strings you think are valid, then try to come up with a regular expression or DFA for the set of all $CSS$ strings, or figure out how to define a subset of $CSS$ that requires non-local checks and unbounded memory (counting, matching, nesting, etc.) If you can define such a subset (like we did for $HTML$ above), then you're good to go.