Switching webhosting

I have a domain name registered with DreamHost and purchased webhosting service with DreamHost, also.

Now, I purchased a different domain name under different registery service.

The question is how do I switch the webhosting service for new domain name (different registery service) from current domain name (w/DH)?

I know I will have to “park” the current domain name.

First, you should go into your account and add the domain name to your account. Even if you already own the domain, you need to associate it with the account where you want to use it. Some domain registrars will not accept a redelegation from your old to your new hosting provider unless the new hosting provider already has the domain in its DNS.

Then, you should contact the registrar of your domain name and arrange to have your domain redelegated (transferred) so that it no longer points to whatever location they have registered, but points to Dreamhost instead. You’ll need to specify the Dreamhost name servers “ns1.dreamhost.com” and ns2 and ns3 .dreamhost.com during this process.

I don’t think you actually need to park your domain in order to transfer it. I have no experience with .com domains (so these instructions might be incorrect!!) but I recently (yesterday) transferred a .dk domain and it had zero downtime; it just went straight from the old provider to Dreamhost.
You might want to check out Dreamhost’s Domainitron.com – perhaps this is useful in your sitation because it handles the US domain types (com net org).