Office 365, make the bold move, stop trying to do what you've always done in the same ways and expecting a different outcome.
It's about doing things in a new way, a better way, a more productive way - and obviously all in the cloud. So if you can do things right in the browser, from any device, that should be your initial, preferred way. yes, desktop app, rich clients apps you will need, but only for more complex tasks. So explore the power of the cloud model from the browser.
Have a look at some of these, re-vamped getting started page to get your head around working with email, calendars, tasks and documents on Office 365 in the Web Apps.
Setting things up correctly
Outlook from the browser
Document management and sites
Questions? Leave a comment, I'm, keen to find out what else you are looking for in terms of getting started and point you in the right direction.