How do I display a hyperlink with an AppleScript?
AppleScript itself cannot display rich text (HTML) in a popup dialog. So your options are:


Display a normal text dialog with AppleScript, showing the URL and asking the user if she wants to go there. If user clicks "OK", open that URL (that's exactly 1 click, so pretty much equivalent to a clickable link).

-- tested with Safari 5.1.7 on Mac OS X 10.6.8
set theUrl to "http://j.mp/LgHoEB"
try
    display dialog theUrl &amp; "\nClick OK to open this URL in Safari." with title "Open URL?" with icon caution
    if button returned of result is "OK" then
        tell application "Safari" to make new document with properties {URL:theUrl}
    end if
on error number -128 -- user cancelled
    -- do something else
end try


&nbsp; 
Use the Safari AppleScript command do JavaScript to make a JavaScript popup with the desired URL as a clickable link (and possibly some more custom HTML):

-- tested with Safari 5.1.7 on Mac OS X 10.6.8
set theUrl to "http://j.mp/LgHoEB"
set JSPopup to "(function() {" &amp; ¬
    "var w = window.open('', 'Clickable link');" &amp; ¬
    "w.document.write(" &amp; ¬
    "'&lt;html&gt;&lt;body&gt;&lt;p&gt;" &amp; ¬
    "&lt;a href=\"" &amp; theUrl &amp; "\"&gt;" &amp; theUrl &amp; "&lt;/a&gt;" &amp; ¬
    "&lt;/p&gt;&lt;/body&gt;&lt;/html&gt;'" &amp; ¬
    ");})()"
tell application "Safari"
    do JavaScript JSPopup in current tab of window 1
end tell


Of course, this will only work if your Safari allows popup windows (with my settings, for instance, a new tab is opened instead).