If you are using the Outlook application on your computer or if you are connected to Outlook on the internet, there are several ways you can disconnect from your Outlook account.
Steps
Method 1 of 3: Sign out of Outlook from the computer desktop

Step 1. Exit Outlook
When the Outlook window is selected, press alt = "Image" + F4 to quit Outlook.
If you want to install Outlook on your computer, you can read this wikiHow article: How to Install Outlook, to get all the information you need
Step 2. You are logged out
After you exit Outlook, you are signed out of your Outlook account.
Method 2 of 3: Disconnect from Outlook on the internet

Step 1. Open a new tab
Open Outlook in a new tab of your favorite browser. Outlook URL is www.outlook.com.

Step 2. Click on your username
Click on your username which is located at the top right of the window.

Step 3. Click on Disconnect
Log out of Outlook by clicking Sign out. The next time you want to check your messages, you will need to sign in to your Outlook account again.
Method 3 of 3: Switch user in Outlook
If you want to change accounts in Outlook, you must have at least 2 different accounts.

Step 1. Open the control panel
If you are using Windows 7, click to start up (at the bottom of the screen on the left) then click on control panel. If you are using Windows 8 open the start screen then locate the control panel.

Step 2. Click User Accounts
In the sidebar, click user accounts and parental security. Then click on mail (e-mail).

Step 3. Add a new profile
In the email dialog box, click show profiles then click on add. Enter a profile name then click OK.

Step 4. Configure the email account
Provide the information requested from you. If you need help, contact Outlook technical support at this link, contact your ISP, or see this wikiHow article: How to open an email account.
Free email services like Outlook, Yahoo, Google or iCloud provide the information you need to set up your account in a personalized way

Step 5. Select the Choose Profile option
In the Outlook dialog box, select the option choose a profile in order to be able to select a user profile and select the user that you want.

Step 6. Click OK
The next time you launch Outlook, you will be asked which user account you want to use.