There are a ton of ways for hackers to get into a network. The biggest security risk is people. You can have all the right security measures in place and someone will mess all that up. Email or phishing attacks are huge. An attacker sends an email with malware attached and then a user clicks on it to get all their free iTunes music and boom the attacker has a foot hold in the network. Social engineering is a big way for attackers to compromise a network

Web attacks are huge too. Mismanaged websites and application are always a way to get in a network. https://owasp.org/www-project-top-ten/ has a list of the top 10 web application security risk that they keep updated and is a great source for that.

A less common way is probably like the movies show a hacker just reinforcing their way into a network.