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 A records
Add each A record for your subdomain like this (substituting your sub domain and IP address):
Configuring CNAME records
Add your CNAME record for your sub domain like this:
Configuring MX records
Add your MX records like this:
Configuring TXT records
Add each of your TXT records like this: