I'd like to begin the certification process and don't know where to start (registration, cost, details of each of the different levels).
You are in the right place... you just need to explore it a bit more
Start with the overview
https://community.esri.com/community/esri-technical-certification/pages/overview
Then
https://www.esri.com/training/certification/
and some content
From there you can clarify this question for further directed information
Great suggestions, Dan!
I would also include the Exam Resource documents as a valuable tool for preparing to sit for an exam. They can be found on the exam overview page and provide detailed information on the topics that will be covered in the exam.