There are many different possibilities to answer this question. We will go top down beginning with the browser.
Most of the browsers support the html input tag of type "email" and most of them would automatically warn the user about a wrong format of the address. However there are many standards of email address pattern. Furthermore the user might disable the browser validation, so we should not rely on this.
The second station is the javascript of the browser. Probably the easiest way to validate the email address is to use a regular expression an match the input against this expression. However the user may disable the javascript or send a request in other way than browser. Therefore it's absolutely necessary to validate the email address on the server side. This might be done by a regular expression, but some more sophisticated systems would check the MX record of the domain given in the email address, to be sure it might be a real address of a real mail server.
Use automated UI Test, which is possible with the Selenium library and a browser driver. The browser driver allows us to run actions in a browser while writing code. The Selenium library is an interface to connect many browsers with the same code base. So now we are able to code a simple test, where a robot is automatically clicking through the website and trying out the login functionality. This technique may also apply to test other important and high priority UI features.