[html] How to run a javascript function during a mouseover on a div

This is badly formed HTML. You need to either have a single id or space separated classes. Either way if you're new I'd look into jQuery.

<div id="sub1">some text</div>

or

<div class="sub1 sub2 sub3">some text</div>

If you had the following HTML:

<div id="sub1">some text</div>
<div id="welcome" style="display:none;">Some welcome message</div>

jQuery

$(document).ready(function() {
    $('#sub1').hover(
      function() { $('#welcome').show(); },
      function() { $('#welcome').hide(); }
    );
});

Javascript

you'd probably want to include the events on your html:

<div id="sub1" onmouseover="showWelcome();" onmouseout="hideWelcome();">some text</div>

then your javascript would have these two functions

function showWelcome()
{
   var welcome = document.getElementById('welcome');
   welcome.style.display = 'block';
}

function hideWelcome()
{
   var welcome = document.getElementById('welcome');
   welcome.style.display = 'none';
}

Please note: this javascript doesn't take cross browser issues into consideration. for this you'd need to elaborate on your code, just another reason to use jquery.