Once you're logged in to your GoDaddy account, you'll see the Products page. From there, just locate your domain and click the "DNS" button on the right to access the domain's DNS zone:
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Once you're in the DNS zone, you will be able to add all the records required for Elastic Email verification:

Now, you will have to specify the type, host and value of the new SPF record.

Type: TXT
Host: @
TXT Value:  v=spf1 a mx include:_spf.elasticemail.com ~all

Type: TXT
Host: api._domainkey
TXT Value: k=rsa;t=s;p=MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCbmGbQMzYeMvxwtNQoXN0waGYaciuKx8mtMh5czguT4EZlJXuCt6V+l56mmt3t68FEX5JJ0q4ijG71BGoFRkl87uJi7LrQt1ZZmZCvrEII0YO4mp8sDLXC8g1aUAoi8TJgxq2MJqCaMyj5kAm3Fdy2tzftPCV/lbdiJqmBnWKjtwIDAQAB

This record will have to have a different type - CNAME.

Type: CNAME
Host: tracking
Points to: api.elasticemail.com

Don't forget to hit "Save" for every record created.

When you are done with setting up your DNS zone, you can verify the domain on your Elastic Email account's Domains screen.

When on the Domains screen, click the "Verify Domain" button, enter it's name in the resulting pop-up and hit Add.
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As a final step, click "Verify domain" (or "Add domain validation" under the three-dot menu first).

Green check marks under the verification will indicate that the DNS records have been inserted properly and the domain is verified successfully.

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