If you haven't checked these out already, there are a couple of links mentioned right here that are both helpful walkthroughs: http://wiki.dreamhost.com/Wordpress#Moving_A_WordPress_Installation
Every WordPress installation has a set of files in the site directory (on the web server), and a MySQL database (usually on another server). When you say the current designer sent the whole site zipped, does it include ALL the WordPress files, as in it is the whole site directory? Do you also have the .sql database backup from the current host/designer? If you have those, no need to install WordPress on our end (nor on your desktop)! You would simply upload the entire site directory you were given, and point the site to it (support can help with this bit as well if needed, it's done in the Fully Hosted settings for the domain in our panel). Once the domain is set up to point to the directory you uploaded, it's time to create an empty database from our panel here:
You will use that new empty database to upload your .sql backup If you don't have that backup yet, please see the article mentioned in our "Move WordPress to DreamHost" wiki: http://wiki.dreamhost.com/Backup_MySQL
Once you have the database ready to upload here, you can follow one of the methods described here (our support can help with this): http://wiki.dreamhost.com/Migrate_MySQL
Once your site directory and database are uploaded, you'll be at these steps to edit the wp-config.php file and set up a test: http://wiki.dreamhost.com/Move_WordPress_to_DreamHost#Edit_wp_config.php
If you need any help with specific parts on our end (like connecting to the database in phpMyAdmin and editing URL values in the _options table to test before the switch), you're more than welcome to ask for help from support for that as well.