By my count, at this point, you are talkling about two (2) "blogs" (one on wordpress.com and one on some domain installed and being served from your DreamHost account - is that correct?
Is the blog you have hosted on WordPress.com being mapped to a domain you own, or is using a "free" something.wordpress.com doamin?
Referring to your first statement, when you say "the domain name I have registered for my blog", which domain name are you talking about (one you have registered but is not in use at present, are a domain that is currently pointing to a wordpress.com blog)?
When you say "my new wordpress location" are you talking about your newly installed WordPress blog on the DreamHost account?
When you used the one-click installer, did you use the "easy" one-click" install (which is "hosted", similar to the way WordPress.com works) or did you use the "advanced" one-click installation (where the files are actually stored on your user space in your account)?
I know ... all questions and no answers, but the information in your question was ambiguous, so the correct answer can't be given until the above confusion is resolved (because how you "point" a domain at a "blog" depends on the answers to those questions).
Irrespective of how many domains you register and where you choose to point them, the first step is to actually register the domains. You can do that via any registrar, or through DreamHost (on DreamHost you register domains via the Web Control Panel -> Domains -> Registration screen(s)). When registering the domains, set the nameservers to DreamHost's nameservers at the registrar (this is done automatically for you as the "default" if you use DreamHost as the registrar). On other registrars, you will indicate/enter ns1.dreamhost.com, ns2.dreamhost.com, and ns3.dreamhost.com as the nameservers to use for the domain.
Once your domains are registered, and your nameservers are correctly set, you need to arrange for hosting them on your DreamHost account. You do this by using the Web Control Panel -> Domains -> Manage Domains screen(s) ), where you select the "Add a Domain or Dub-domain" link/button/bar near the top of the page.
For each of the "websites" you want to host, "Add a Domain" using one of the domains you have registered by completing the screen described above and submit it by clicking the "Fully Host this Domain Now" link. Repeat as desired for the additional websites.
[color=#CC0000]NOTE:[/color] Pointing multiple domains to each website is a decidedly bad idea no matter what you may have been told by supposed "SEO experts". While it may seem that it would be nice to have a user find your site (the same site) whether he/she types "yoursite.com", "Yoursite.net", or "someotherlikelychoice.whatever," the fact is that even if you do this so that it still "works" (all relative links, etc.) once the user has gotten there using one of your domains as the url, Google will penalize each of your "sites" for having identical content. They will identify this ploy as a "search engine gaming" technique and your overall search engine position and page rank will suffer.
Additionally, if these are to be WordPress, Joomla!, or one of many other common web applications, the rewrite rules that drive those sites will prevent you from using this (bad!) technique.
All that said, you can do that, if you are bound and determined to do so in spite of the consequences, by "adding" the additional domains in the control panel (as described above) and setting the directory in the "Specify your web directory" to the same directory as the existing domain you want the additional domain to "point" to (set up previously as described - fully hosted). Alternately you could add these additional domains and use the "Mirror an existing domain" hosting method further down the page.
Each of these methods present a problem of one sort or another, and generally I do not recommend that you use them unless you fully understand the ramifications of those problems and are equipped to deal with the consequences.
A better approach is to add each of these additional domains as "Fully Hosted domains" of their own, and install apache redirects, that you can control and customize, to redirect the users arriving at that domain to the single domain with the content. If you feel that this is beyond your capabilities, the "next best" approach is to "add" them using the "Redirected" section of the form, re-directing them to the site(domain) with the content. This has generally the same effect as the first method described in this paragraph, but DreamHost establishes the re-directing mechanism for you (which means you don't have to mess with it, but you also cannot customize it to the same degree as you could if you handled the redirects yourself from a "fully hosted" domain).