In your quote_randomquote template, find:
HTML Code:
<tr><td class="alt1" width="30%"></td>
<td class="alt1"><div style="font-style:italic;margin-right:10%;">
<p>"$randomquote[quote]"</p>
<p style="font-weight:bold;margin-left:25%;">
The 30% represents the margin on the left, the 10% is an additional margin for the quote amd the 25% is the margin for the author. You can adjust these numbers until it looks good. You probably want the margins instead of just centering it, since a centered multi-line quote looks weird.