What is the best way to map mail.mydomain.com to https://www.google.com/a/mydomain?
Google provides a tool for this that will redirect mail.yourdomain.com (or whatever you choose) to the login page for a service. More info here: http://www.google.com/support/a/bin/answer.py?answer=53340
It might take 48 hours for your http://mail.mydomain.com to actual show google apps mail because of slow DNS propogation of the provider
One way to go is to do as mfarver suggests. That works. In this case, you'll need to make a CNAME on your domain (i.e. mail.mydomain.com in your example) and have this CNAME point to ghs.google.com.
Another and IMHO slightly simpler way is to set up HTTP redirection with whoever hosts your DNS. Godaddy, Gandi, Easy DNS, and many more have this -- but I can't tell you exactly how to set it up, since each of these has their own user interface. But search the documentation with your DNS host, and you should find it. In this model, you only set up
Tip: Be sure to set up the redirect so that it points to HTTPS (i.e. SSL encrypted), and further set the option to always require SSL encryption inside the Google Apps administration interface. For security reasons you shouldn't permit your users to have non-encrypted access to Google Apps.
Lastly, I have refrained from editing your question, just in case I could have misunderstood something. But didn't you mean Google Apps email, and