Are you moving your domain’s email to google apps, or just forwarding to email@example.com or something similar?
If you’re just forwarding, then you can change your email to a forwarder and it won’t keep the email at DreamHost.
If you’re talking about switching to Google Apps email, it’s not ‘easy’ nor does Google explain it well
I ended up using the temp alias of firstname.lastname@example.org and having all my new emails sent to yourdomain.com forwarded there instead.
Then I opened up both my email on my server and google as email@example.com (yes, the ‘real’ email address) in my mail app, and copied over all my emails to the Google account.
Once that was done, I changed my email to forward to firstname.lastname@example.org
Finally, I changed the MX records to use google and not my server.