On Hover DNS tab, add new record:
Hostname: mandrill._domainkey
Record Type: TXT
Value: PASTE IN THE KEY FROM MANDRILL, BUT REMOVE THE SLASH BEFORE THE SEMICOLONS (http://help.mandrill.com/entries/21681347-how-do-i-set-up-sending-domains)
Takes a few minutes to propogate, but you can test it with:
dig mandrill._domainkey.YOURDOMAIN.com TXT
If that shows the correct key, hit the Test button in Mandrill (under Sending Domains) and make sure it says Valid.
Thanks so much for this @swanson. For those curious, the console output of the command
dig mandrill._domainkey.YOURDOMAIN.com TXT
should look something like;