Where do I get advice and guidance from in my PhD if my supervisor is not an expert in the field I am working on?

1. From your question, I understand that you should be on good terms with your advisor. Then, I think you should be straightforward and ask him to connect you to some other experts in the field. Perhaps, you could even have one of them on your committee as your co-advisor.
2. You could probably ask the other professors at your current or even the previous department for some help. Personally, I'm always happy to help students previously in my classes.
3. If your university regulations permit, you could take a short sabbatical (usually 3-6 months) in another university under the supervision of a professor expert in your desired field. If you are in the early stages of your Ph.D. studies and the regulations require you to be a 3rd- or 4th-year student before taking such a leave, you could still talk to your possible choices and seek their help. Then when you officially take the sabbatical, you could work closely with them.
4. There are lots of online groups and websites dedicated to helping people having questions similar to yours. Being an active member of them would benefit you greatly in the long run.

Paradoxically, you will probably get the best help connecting with others from your adviser. He will know people, and he can make the necessary introductions with others to ensure that you get replies to your questions if you are asking random people you have otherwise never met.

In some fields, such as Computer Science, conferences are a very important way for people to publish, but also to meet and form working relationships. Perhaps you can manage to attend a conference in which others in the field are likely to be present and socialize a lot. Attend talks and speak with other attendees as well as the speakers.

Perhaps you can get a few ideas at such a conference, but the goal is to form a correspondence with such people.

Ideally, if you could attend with your professor and exploit whatever personal relationships he has already developed. Get yourself introduced to others.

But it may even be possible to obtain introductions through your professor without such travel to conferences. Many people work collaboratively across national boundaries via email and such.

And don't neglect other faculty at your university who may have developed relationships with some of the people whose papers you read - or with their professors.