to summarize quickly what's involved, you're going to have to log onto your control panel with your previous host and create a database dump of your wordpress database. You can do this via phpMyAdmin if you have access to it, or other tools provided by your web host. Consult your previous web host's documentation to find out the details in case you get stuck.
Once you downloaded the database dump to your local PC, log onto your dreamhost control panel and create a new mysql database for your wordpress installation. Access the new database via phpMyAdmin through the dreamhost panel. Then, insert the database dump that you saved in a file on your local PC into the new (blank) database on the dreamhost server. For details on how to do this, consult the phpMyAdmin documentation. You should also be able to find this information in the dreamhost wiki, as well as many other support forums.
Next, you need to transfer your wordpress installation's files from your previous host to your new dreamhost account. You can do this either by downloading them to your pc first and then uploading them to dreamhost via FTP/SFTP or by logging onto your dreamhost account via SSH and pulling the files from your other server via FTP/SFTP directly to your dreamhost server. This can be much, much faster, especially if you have a big installation, so if you are even vaguely familiar with the Linux command prompt, you should try and pursue this option.
Regardless of what you end up doing, the whole process will be sped up significantly if you archive and compress your old wordpress installation prior to transferring it. To do this, you can log onto your old webhost's server via SSH, if they provide SSH access. If not, they might provide a tool via their panel that allows you to create a backup of your files on the server, which should allow you to download your entire directory(s) as a single .tar / .tar.gz / .zip file.
The best method would be to then upload the single file to your dreamhost server and logging on via SSH to decompress it on the server.
If executed correctly, this whole operation can be done in under 5 minutes.
After you transferred your files and your database, you'll have to edit at least one file in the wordpress installation's directory to modify the login information for your new database. Chances are that the new database that you set up on your dreamhost server will have a different name than then one on your previous host, as well as a different username/password. If you can manage, however, to note this information from your previous host's contorl panel, you might be able to name your new dreamhost database exactly the same as your old database, and you might also be able to set up the same username/password combination for the database user account that wordpress will use to access your database, and you'd therefore be able to skip this step.
Lastly, after you verified that everything is working on your dreamhost account, you'll have to point your domain name to dreamhost's servers. Note that you don't need to transfer your domain to dreamhost, you only need to reconfigure its name servers to point to dreamhost. In order to do this, access the service provider with whom you registered your domain. If you're not sure who you registered with, you can often find that information by going to http://whois.net and entering your domain name in the search field. Access your registrar's control panel (might be different from your webhost, but doesn't have to be), and reconfiguring your name server settings. You'll need to set your name servers to n1.dreamhost.com, ns2.dreamhost.com, and ns3.dreamhost.com. The change can take up to 48 hours to take effect, but often this happens sooner.
If you've done everything correctly, your domain will now bring up your wordpress installation on your dreamhost account. If you need to check if the domain is pointing to the right server, upload a text file to your domain's root directory on your dreamhost server (but not your old server) and try to access that file via a web browser. If it's there, that means your domain is now pointing to the right place!
On a side note, you may want to make sure that no edits will take place on your wordpress installation during the 48 hour waiting period, since any changes you make / any new content you add will not carry over to your dreamhost account unless you re-transfer the database as described above after your domain has transferred successfully. Also note that the easiest way to access your site's files during the transition period is by entering the your server's IP address as the hostname in your FTP/SSH program, making sure you note the correct IP address that is associated with each respective web hosting account.
Hope this helped... good luck!