How would I use javascript to validate an e-mail with output on the DOM?

Basically I created a form in html and when things are input properly it simply goes to google.com. Right now I have completed the first few fields but I am unsure of how I would make it recognize if recognize that something written improperly in email field does not include an '@' sign and a '.' somewhere after it.

I created a fiddle as I was having trouble getting some of the longer of my lines of code to be in-line which is weird considering I ask questions a lot and this is the first time it has ever happened.