In the top right, click Settings (the gear icon) > Settings.
Click the Accounts and Import.
In the Grant access to your account section, click Add another account.
Enter the email address of the person you want to add and click Next Step.
Click Send email to grant access. The person you added will get an email asking them to confirm. It may take up to 24 hours for you to see them as a delegate after they confirm.
Make Gmail look more like Outlook
Click here for a guide on switching from Outlook to Gmail. It includes a couple ways to make Gmail feel more like Outlook.
Official Google Guide to Gmail
Click Here for a full "Getting Started with Gmail" guide