For your existing sites:
1. Add hosting for the two domains in your DreamHost panel using Domains>Manage Domains>Add New Domain / Sub-Domain. You want a fully hosted domain. This will also create the web directory for these domains under your user account.
2. Upload the sites to the directories that were created for you in step 1.
3. Use the information in the Viewing Site Before DNS Change page on the DreamHost support wiki to... view your site before making any DNS changes.
4. If everything looks good, switch the nameservers for your domain to ns1.dreamhost.com, ns2.dreamhost.com, and ns3.dreamhost.com.
For the new site, I had a few questions. Is your developer going to continue to maintain the site or is he just going to program it and then leave it to you?
You actually have three choices:
1. Give him your username and password for ftp access for a while. This has obvious downsides, even if you change your password afterwards.
2. Create a new username as password for him. This isolates his account from yours, but the new domain will be hosted out of his home directory rather than yours so if you're eventually going to take it over, you'll have to remember that it's over in the other home directory.
3. Do 2, but copy everything over to your home directory after he's done.
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