Outlook on the web relies on your web browser for checking spelling. That's why you don't see a spell check button or spelling settings in Outlook on the web.
Spell checking is available in Internet Explorer 10 and later versions, and current versions of Firefox, Chrome, and Safari. Check the options for your web browser to learn more about how to use it to check spelling.
If you are using Outlook desktop client, you do have the ability to use spell checking feature. Learn more.