If you're familiar with the Google Apps admin interface, this should be fairly easy to setup. It's not always obvious where to find these settings, so I've created a step-by-step outline of what to do.
How DomainKeys Identified Mail (DKIM) works:
Your outgoing mail server uses a private key to generate a digital signature and embeds that signature in your message. The recipient's mail server grabs the public key from DNS and uses that public key to verify your signature.
Step 1:
Login to your Google apps admin console and click on the Google Apps icon.
Step 2:
Select Gmail.
Step 3:
Select Authenticate email.
Step 4:
Under Authenticate email, select the domain you want to authenticate. The current status next to the domain will be Not authenticating email.
Click on the Generate new record link.
Step 5:
In the pop-up box, the Prefix selector will default to the word Google. You can use any prefix, but leaving the default is fine.
Click the Generate button.
Step 6:
Copy the key.
Step 7:
Create a new TXT record for your domain. In this example, we're creating a new TXT record for Google._domainkey.hedgehoghosting.net
If you don't manage your own DNS, ask your provider to create a TXT record for the hostname Google._domainkey using the key you just generated.
Step 8:
After your TXT record has been created, click on the Start authentication button. You should now see Status: Authenticating Email next to your domain name.
That's it. Your e-mails will now have a digital signature that all DKIM enabled mail servers can use to authenticate your message.