You can use the filters in your customer base to send a newsletter to your customers. Then export the filtered segment to Mailchimp. You can also export your whole customer base.
Then go to your Mailchimp account and click on "Manage Audience" and "Import Contacts" to select the CSV file. Click on "Continue" in the lower right corner of your screen.
On the next page, you can select the file from your computer that you want to import into Mailchimp. Then select "Continue To Match" in the lower right corner of the screen.
The next step will involve matching the columns by clicking on "Edit" and later on "Save". Then click on "Continue To Organize".
Lastly you'll add a tag to your new list so that you can easily find it when sending a new e-mail. Click on "Continue To Review" to round off the import process on the last page.