Hi James, welcome to Microsoft Q&A! Nice to see you here. :)
To open a developer account, please refer to this document: Steps to open a developer account.
The registration fee varies by region and account type (individual/business). You can learn about the differences here: Types of developer accounts. For specific fees and locations, check this document: Developer account fees and locations.
Feel free to accept my answer if it helps — it may help others with the same question. :)