Get data from a data source
Create a Data Blend that will get a list of contacts from a certain data source, e.g. MySQL or a CRM.
Sync to a MailChimp list
Add a "loop" Block in your Data Blend, and inside this loop use the MailChimp Block "Add or update a list member" to send this contact to a MailChimp list.
Schedule your Data Blend to run e.g. each day.
Configure a campaign in MailChimp
Create a campaign with a trigger "A subscriber joins your list, LISTNAME."
Make sure to check the checkbox "Trigger when subscribers are imported".
Important: make sure to create your campaign AND BRING IT LIVE (e.g. in status "paused"), BEFORE you start adding contacts to the list in MailChimp using Blendr.io.
This is because the campaign will only process contacts that were added to the list AFTER the campaign was created AND AFTER the campaign was put live (meaning not in status "draft").