Email security is the most important because hackers can often get to all of your other accounts by requesting passwords, which then get emailed to you. Some services also offer Two-Step Verification, which often means you need a code that is texted to you, in addition to your password. Here is how to add security on some of the most popular online services.

Gmail:
Go to this page and run the Security Setup.
https://myaccount.google.com/?pli=1

Yahoo Mail:
Consider turning on 2-step verification for Yahoo Mail. https://help.yahoo.com/kb/turn-two-step-verification-sln5013.html

Facebook:
Turn on Login Alerts and/or Login Approvals. https://www.facebook.com/settings?tab=security

Twitter
Go to this page and consider your options in the top Security section. https://twitter.com/settings/security