I am fairly new to web development and have never used Digital Certificates before. I assume using a digital certificate on a silverlight web page is the same as using one on any other web page, but i thought i should check. There are a few example of digitally signing the .xap file on the internet, would it then be a case of simply buying the certificate (from verisign or somewhere similar) and distributing it to customers?
It sounds like you're confusing code signing with serving content over HTTPS.
Signing your code lets people know that it really was you that wrote it, and can trust that it hasn't been tampered with by anyone else.
HTTPS allows a web client know that communications between it and the web server are secure from snooping (exception being when the client is configured to go via a proxy server, which could be malicious).
You can use both independently, or together. For any "shrink-wrap" style software release, I would recommend signing your code. If you handle any sensitive data on your website, such as credit card details, then you should handle this data only over HTTPS (I believe most credit card companies require this in their terms and conditions anyway)