I'd spend a bit of time, like several hours, reading about the concepts and purpose of the new tool. What does it solve and how?
Then I'd just jump in and start using it. If it's interesting enough I'll do something at home, but otherwise just use it at work and look up any problems.
(Although, if the team is switching to a new technology, chances are I'm one of the people who has been pushing for that for a while, so perhaps I'm already familiar...).