When setting up email for Office365 on your Android phone there may be a number of "slightly" different screens.
In these examples, I am using and HTC One-S phone on Android 4.x (ICS). Overall the process is very similar for all androids.
This guide should get you through, but read your screen as you proceed and getting around any differences should be pretty straight forward.
Go to Settings
Slide your finger from the top of the screen down to reveal the notification window.
On many phones this is a gear icon with no words on it
Look at accounts
On the next screen choose Accounts and Sync
Add an account
Click the Add button on the accounts screen
Let your phone know what type of account
Select Exchange ActiveSync from the account types screen
Your Email Info
Enter your COMPLETE email address
Your email should show in the first field as you entered on the last screen
make sure your server is set to m.outlook.com
Enter Username info
Scroll down a bit to see username Fields
When to sync
If you are prompted for Smart Sync, I recommend using it. This is a great feature that monitors when you touch your phone and determines when you are sleeping not active etc, and will not even try email unless you unlock your phone during that time.
Name your account
Give the Account a Name you will recognize (No one sees this but you)
Click Finish Setup
You are done
Your email will now process and sync
Some carriers will have their phones send a message that some security settings may need to be controlled by the email.
It is ok to press the Next or OK prompt on this message
My guess is you have hit a few screens that weren't exactly the same, but... you got to here, so assume you are done.
Good work, note that you can delete your mail anytime and re-add it, Exchange is much like google mail, nothing is stored "Only" on the phone, so you get it back just by syncing back.