Office 365 works best when everybody on a team has an Office 365 account – and your account is access to EVERYTHING in Office 365, it is your identity, and when it comes to working in the cloud, your identity and the security of that identity is really important. You can share mailboxes, calendars, files, collaborate in real-time online, see/manage team members presence, chat, video conference and much more!
Office.com a.k.a - Portal.office.com
There are a few different ways to login to Office 365, perhaps the best is navigating directly to the Office Portal. Open a web browser and navigate to
https://office.com/. This will take you directly to all of the Office 365 applications your administrator has configured for you. (The exact applications available to you depends upon the type of license your user (identity) has assigned to it. If you are unsure contact your administrator.)
If this is the first time you have accessed the web portal you will see a screen similar to this one. Click "Sign In".

Sign In
Once you click the sign in button on the previous screen or if you browser recognizes you have been to the office portal before, you will be asked to enter your email address.
Personal or Work/School?
Microsoft provides two types of accounts. There is a Personal Account and there is a Work or School account. Unfortunately these aren’t the only two names that these accounts go by. Personal Accounts are also called Live IDs or Microsoft Accounts. Work or School accounts are also known as Office 365 accounts, organizational accounts or even Azure Active Directory accounts. However, PERSONAL accounts are accounts for consumers to use and log into consumer level services such as regular Skype, Xbox Live, or Outlook.com. WORK/SCHOOL accounts are accounts that are given to you by your work or school. And you’ll primarily use them to sign into the Office 365 services for business purposes.
To add a little more confusion, you can have the SAME username (identity) for each type of account. It is VERY important to choose the correct type when logging in via the office portal.
Multiple Accounts
If you have logged into different Office 365 accounts using your web browser instead of seeing the Personal and Work/School options in the previous screens you will be faced with a choice of choosing which office account you want to login with. (See below)