Over last two years I have passed a bunch of Esri technical certification exams (10 exams to be precise). Esri did a great job posting multiple blog posts regarding how to prepare for the certification: there is a free training seminar covering the details and some blog posts and Esri Australia blog post. Esri has also authored two special instructor-led courses for those who plan to become certified as ArcGIS Desktop Associate and ArcGIS Desktop Professional:
Esri Technical Certification: Skills Review for ArcGIS Desktop Professional
Esri Technical Certification: Skills Review for ArcGIS Desktop Associate

Another useful resources are free web courses (2 for Deskop and 1 for Server):
Esri Technical Certification: Sample Questions for ArcGIS Desktop Associate

Esri Technical Certification: Sample Questions for ArcGIS Desktop Professional

Esri Technical Certification: Sample Questions for Enterprise Administration Associate

I highly recommend going through sample questions to get an idea of what…