If you can get to the /admin console, in the email section there is a “Send Test Email” button and input box.
Send yourself an email from there – when it arrives look at the headers. If it is good you should see stuff like this:
Received-SPF: pass (google.com: domain of bounce-md_30025788.5329e912.v1-b00d7b34ebd241fe92b942873ea61686@mandrillapp.com designates 198.2.128.129 as permitted sender) client-ip=198.2.128.129;
Authentication-Results: mx.google.com;
spf=pass (google.com: domain of bounce-md_30025788.5329e912.v1-b00d7b34ebd241fe92b942873ea61686@mandrillapp.com designates 198.2.128.129 as permitted sender) smtp.mail=bounce-md_30025788.5329e912.v1-b00d7b34ebd241fe92b942873ea61686@mandrillapp.com;
dkim=pass header.i=noreply@codinghorror.com
The key phrases are spf=pass and dkim=pass and SPF: pass.
The body of the email does explain all this.