You can use an XMLHttpRequest object to do this. Here's a simple example
var req = new XMLHttpRequest();
req.open('GET', 'http://www.mydomain.com/', false);
req.send(null);
if(req.status == 200)
dump(req.responseText);
Once loaded, you can perform your parsing/scraping by using javascript regular expressions on the req.responseText member.
More detail...
In practice you need to do a little more to get the XMLHttpRequest object in a cross platform manner, e.g.:
var ua = navigator.userAgent.toLowerCase();
if (!window.ActiveXObject)
req = new XMLHttpRequest();
else if (ua.indexOf('msie 5') == -1)
req = new ActiveXObject("Msxml2.XMLHTTP");
else
req = new ActiveXObject("Microsoft.XMLHTTP");
Or use a library...
Alternatively, you can save yourself all the bother and just use a library like jQuery or Prototype to take care of this for you.
Same-origin policy may bite you though...
Note that due to the same-origin policy, the page you request must be from the same domain as the page making the request. If you want to request a remote page, you will have to proxy that via a server side script.
Another possible workaround is to use Flash to make the request, which does allow cross-domain requests if the target site grants permission with a suitably configured crossdomain.xml file.
Here's a nice article on the subject of the same-origin policy: