You can purchase a domain registration at any company you like, however it's recommended that you purchase it at DreamHost:
This makes it easy to control your hosting and registration at the same location (the DreamHost panel). You can also purchase the registration at another company, but still host your site at DreamHost. This article explains how to go about this.
This article assumes you've already purchased your domain registration at another company.
Adding a hosting plan
In order for your site to display online, it must be set up on a hosting plan. This puts it on a web server so anyone in the world can view it. View the following articles for information on how to add a hosting plan and add your site to it.
Add your site to your hosting plan
Now that your hosting plan has been added, it's time to add your site to the plan. This adds the website to the DreamHost webserver so it can be seen on the Internet. View the following article for information on how to add a domain to your hosting plan.
This only tells the server to serve this domain name. You must still point your DNS to the server so it displays online.
Pointing your DNS to DreamHost
When you originally purchased your domain registration at another company, the DNS settings were most likely set to that specific company. In order for your site to be hosted on DreamHost's servers, you must change the DNS settings for your registration to point to DreamHost.
View the following article for instructions on how to point your registration's DNS settings to your DreamHost server:
Waiting for the DNS to update
After you change your DNS settings, you must wait until they update online.
If you changed your nameservers, this could take 24-72 hrs to fully update.
If you changed your A record, this should only take 4-6 hrs.