Windows 10 has the Outlook Mail and Outlook Calendar apps already built in. To find them, go to the All apps list by swiping over from Start. If you know you'll access them frequently, pin them to Start if they aren't there already.
Email and scheduling rockstar
You've found the apps, now make them useful by adding your accounts. If this is the first time you're opening either of the apps, you'll see the Welcome page. Follow the instructions to set up your account. Otherwise:
In the Mail or Calendar app, select More at the bottom right.
Go to Manage accounts > Add account, choose your account type, and then follow the instructions.
Your mail and calendar start syncing as soon as your account is set up.
A couple of other handy things you may want to know:
After you've calmed down from the excitement of adding one account, you can go back to More to add more.
Delete an account at any time by going to More > Manage accounts, selecting the account you want to delete, and then selecting Delete account. (If you've signed in to your phone with a Microsoft account, that account is added automatically to the Mail and Calendar apps and can't be deleted. But you can remove any others you added yourself.)
If you have more questions about how to use the apps, including troubleshooting info if you're having problems adding an account, find answers by going to More > Settings > Help. (Then select Open Help in the Mail app.)
Where are my contacts?
When you add an account, either through the Mail and Calendar apps or other social media apps, any contacts associated with those accounts will show up in the People app. Find the People app by swiping over from Start to the All apps list.