Firstly you'll need to go to the branded domain page under settings within your Airship account to generate the DNS records, here's our support article to help with this.
Once you have the DNS records, within 123-reg's control panel, you will need to use their Advanced DNS tool >
Configuring TXT records
Add each of your TXT records like this:
Configuring CNAME records
Add your CNAME record for your sub domain like this: