This article does not apply to DreamPress as you are only able to add one domain per service with that plan. You can read more about it here:
Is there a limit to how many domains/subdomains I can add to my panel?
No. There is no limit to how many domains/subdomains you are able to add to your DreamHost account with shared, VPS, or Dedicated hosting.
Do I have to create a new directory if I add a domain?
No, you do not.
A new directory automatically appears (in the name of your domain) in your users directory within fifteen minutes of adding the domain. You don't need to create a new directory yourself.
When somebody visits your website, the configuration files for the DreamHost web server tell the visitor to go to the new directory. When you add a new domain and specify its directory, the panel adds the necessary lines to the necessary config files on the web server. There is no need to for any other configuration other than adding the domain in your panel.
How much is it for an extra domain?
All hosting plans at DreamHost (excluding DreamPress) allow an unlimited number of domains and subdomains.
If you want to host an entirely new domain, you can register it on the (Panel > 'Domains' > 'Registrations') page or through any other domain registrar (although, remember that registration costs may vary).
Does an extra domain have to point to the same place as the original domain?
No, but it can if you'd like it to.
It can point to your existing site, or it can point to an entirely different directory. When adding the domain in your panel, you get to decide where it points.
Does an extra domain get its own storage space, login, email aliases, and so on?
Your extra domain gets its own email addresses.
You can also use the same username as your main domain, or you can create a new username. All web files for the domain are stored under the user you assign to it. But, please note that the amount of space allotted depends on your hosting plan. For example, when you purchase a VPS plan you must choose how much disk space you’d like the user to have.
You can view more information about VPS plans here:
What if I already have a registration at another company?
If you've already purchased a registration at another company, you can point your DNS to DreamHost. After the DNS is pointing to DreamHost, the domain you've added hosting for will be hosted at DreamHost. View the following article for information on what DNS records you should point to.