There are a lot of useful apps out there - these are a few we think work well for students at our school:
Gmail - all students have a school Gmail account. Using an app to manage your messages is super convenient.
Google Drive - students also have Google drive where they can store files, create documents and presentations, and do other stuff.
QuickOffice - another free Google app, this one lets you edit word documents and make new docs when you're offline. It can talk to Google Drive.
Google have also recently split some of the functions of Google Drive off into separate apps, called Docs and Sheets.
Your google calendar is also a very helpful thing, and there's a handy app for that too.
And for PCs, Open Office is a free, fully featured software suite which lets you make documents, spreadsheets and stuff.