I was wondering, how would you destroy a session of the first person if someone logged into the same account of a certain website using another browser on the same computer or a different computer all together?

This has nothing to do wth MYSQL, but:

1. Jou would need to store user_id & session_id into app global variable (array)
2. check when new user logs in
3. at least in java: oldSession.setMaxInactiveInterval(1)

that would destroy old sessin in a second.