If you use Google Apps to access your MailChimp account, you'll need to set up a username and password with MailChimp.
After you have a username and password, you can use those credentials to connect MailChimp to Zapier.
When using the Add/Update subscriber action to create a new subscriber, use data from a previous step when filling the Subscriber Email field. This ensures that the Zap will use the current email address. If you type an email address on the field, it will try to subscribe the same email address every time.
If you cannot see some fields from your MailChimp account on the Zap editor, scroll to the bottom of the MailChimp step and click Refresh fields. This will update the list of fields available on the Zap.
If your MailChimp list has double opt-in enabled, you won't see any subscribers added by your zap until after that new subscriber clicks through the double opt-in email. However, your task history will show a successful task immediately, even if the subscriber does not confirm the double opt-in email.
MailChimp checks for duplication based on email address, so if your zap tries to add an email address that already exists in that list, that task will appear as "halted" in your Zap run history. If you'd like to update a subscriber, select Yes from the dropdown menu of the Updated Existing field, in the Set up action section of the MailChimp step.
If someone was subscribed to a list, then unsubscribed, and later was added back to the list, the Zap will not trigger as it sees it as a duplicate from the first time they subscribed. Unique email addresses will only be sent once.
Your Zap may also not trigger as expected if subscribers are imported into MailChimp. In these cases, it's possible to bulk import data into Zaps.
You can look at the Source field on a subscriber record, in your MailChimp list, to see how it was added.
At the moment, Zapier does not have an action that sends a campaign to a specific person. The Send Campaign action will email all contacts in your audience.
To trigger a campaign for each new subscriber, you can set up up an automation email in MailChimp. Create a rule that sends an email whenever a specific tag is added to a subscriber. Once that's set, create a Zap using the MailChimp Add Subscriber To Tag action, which will trigger your automated email.