It looks lilke you are "getting there" but a few clarifications appear to be in order, so please bear (patiently) with me:
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For just the sake of getting support and being able to do the eventual updates, I should do it "right".
I agree, but one note of clarification re "updates". From looking at your space (in the past while you were testing, you exposed a directory listing at one time) I noticed a ".old" directory. This indicates you originally installed Joomla! via the Control Panel's "One Clilck" mechanism. Wthout confusing things even further, if you want to *preserve* the ability to "upgrade" via "One-click", you *cannot* (if at all - the "one-click" back-end is not public, so I can't tell exactly how it works when executing an upgrade!) use the method we are discussing - the "One-Click" installer will not recognize your "moved" Joomla! as being one of its "progeny".
This leaves two alternatives: you can preceed as we are discussing, but will have to upgrade "manually", using Joomla! provided upgrade precedures (joomla.org), *or* abandon this approach and just create a new "One-Click" install in the new hestakaup.com directory where you want to host the site. If you choose this second approach, you will not need to worry about modifying any configuration.php or .htaccess file(s), but you *will* have to re-install your chosen templates and components into Joomla!, and move your exisiting data into the new installation. That could be problematic, given your understanding of the issues involved (it *is* complicated by the fact that your compnents affect the data base, as well as your contents) and you can easily end up with a databse that has "parts" of each of the Joomla! installs in it, which is a "Bad Thing"tm - and the site will break.
The process of "manually" upgrading Joomla! (at least in the present 1.0.xx series) is not hard, but will involve more work in the shell/ftp (which you will have to learn how to do eventually if you take this approach, and *should* learn anyway to make your life easier!).
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I have the further option of testing the change before I change the DNS at GoDaddy. That would make me feel ever so much better.
Actually, no. What it does allow you to do is to keep your existing site "visible" via the old " DNS" until you have gotten everything ready to go. I must not have been clear about how the DNS works - if you take this approach you will not be able to see the results in place at hestakaup.com until the DNS propagates and allows your new directory contents to be displayed - there will be no way to "see" that directory from the web unless you connect it via DNS.
There is a "workaround" for this, which is well detailed in this wiki article describing how to view a site before DNS changes, but that process adds an additional series of steps to your project. Again, we are shooting at a "moving target" here - "testing" the site "live" beore making it public entails a different approach.
One way to do that would be to follow the process I've described, but doing it using a sub-domain described in the wiki. Another is to modify your process slightly and "copy" the existing Joomla! installation (directories, files, everything!) to a newly created (via the panel) subdomain of a site that already has DNS in place (such as dev.shirson.com, test.shirson.com, anythingyouwant.dreamhosters.com, etc. - same thing really, but maybe easier to understand). Modify your configuration.php. then "test" your new installation (using the url of the "testing" sub-domain) till you have it right.
Once you are sure it is ready to "go public", just rename the "testing domain" directory (it will be in *your* user space, just like the existing "shirson.com" directory) to "hestakaup.com", correct the configuration.php appropriately, the go to the Control Panel Manage Domains screen and "edit" as needed to make sure that "hestakaup.com" points to the (newly renamed to!) hestakaup.com directory that *now* exists in your "shirson" user space.
Notes on the "To Review" section of your last post:
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1. I figure out how to make the new directory, so I will have a shirson.com/hestakaup.com/.
Not quite, but close. Make a directory so that you will have a hestakaup.com *and* a shirson.com directory in your "base" user space (/home/shirson/shirson.com *and* /home/shirson/hestakaup.com). Doing what you described would just duplicate the issues of having hestakaup.com living "beneath" the shirson.com directory in the tree, which is what you have now with the "shirson.com/joomla" directory; tyring to avoid this is the whole reason we are "doint it right", instead of just using the existing Joonla! directory and pointing hestakaup.com to it 
.
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2. Get into the shell. That through the Wiki. But I have been trying to figure out how to get in for about a 1/2 hour and cannot! Any hints? This is an illustration of what I was ranting about before. Once you get in to the shell, you never forget. But for the first timer it is hard to figure out how to get in.
I'm not sure what Wiki articles you are reading, but you need to use an "ssh" client program to "get into" the shell. Which client program you use will depend upon what operating system you are using. The main Dreamhost Wiki article on the shell includes links to the sections on obtaininng the appropriate ssh client, connecting, and using the shell as well as links to using commands in the shell and other related resources. Once you connect, you should feel right at home, as the shell operates (with different commands, of course, and a *lot* more power) much like the command line you used in the CP/M.
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3. In the shell, use the cp recursive to copy all the files under shirson.com/joomla/ to shirson.com/hestakaup.com/ (by the way, does it need the .com? couldn't it just be shirson.com/hestakaup/?
No.
See item #1 above. you want to recursively cp everything from /shirson/shirson.com/joomla/ to shirson/hestakaup.com/. your "directory tree" should look something lilke this:
---- hestakaup.com/
:
/home/shirson/ ---- shirson.com/ ---- Joomla/
When you have the recursive copy done correctly, all the files and directoryies that are now in "joomla" will be in hestkaup.com
I suppose you could omit the .com, but I advise against it, as this structure makes it clear that a "site" lives in this directory, since you can have many site hosted (at no additional charge for the hosting!) at Dreamhost and you may want to build others.
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4. Then go into configuration.php and change all the instances of shirson.com/joomla to shirson/hestakaup.com
Pretty much correct - though I'll qualify that a bit. You should only have to change the "$mosConfig_live_site =", the "$mosConfig_absolute_path =", and the "$mosConfig_cachepath = " settings. Two of these are "paths" and one is a "url", so you statement is a little over simplified, but you have the right idea. Change the paths to reflect your new setup, and the url to reflect your new url. You will probably also want to change (either through the Joomla back-end", or in the configuration.php file the email address to use for you admin functions (as you are now using a "new" domain - but that is minor, and is up to you depending upon how you want to handle it.)
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5. Test the result by enterning shirson.com/hestakaup.com/joomla
and J! should come up?
Again, re-reading this, and the previous, post should help you realize that there are several problems with this - both in the "testing" methodology and the paths/urls involved. When I wrote that you could make sure everything was properly configured before changing the DNS, I meant you could make the cp and configuration edits first - not that you could "browse" via http and see the changes immediately. However, if that is what you want to do, I've discussed ways to do that earlier in this post.
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6. Change the GoDaddy to whatever DH needs for DNS.
Correct!
All in all, you have it "pretty close to right", with the exception of grasping the *nix directory structure, how that is related to how the domain is set-up as "fully-hosted" at Dreamhost, and the need to use DNS to "browse" those directories. You've almost "got it", I hope.
--rlparker
. I think you and I are both trying to tell him the essentially the same things, though in different ways and with different approaches. I'm gonna step back a bit and see if you can communicate what's involved more effectively than I can - I'm trying my best but do not seem to be getting through. Thanks for jumping in and helping!