I am just getting started in computer science field. And I am interested in a job as a Web developer. What languages should I learn and must good at?

I would agree that you should start with the mark-up and scripting languages (HTML, CSS, Javascript, and JQuery - which is not a language, but a code library written in Javascript to make cross-browser scripting easier). For the server "business logic" code, I am a C# developer, but there seems to be higher demand for PHP due to several popular CMS systems that are written in PHP and need customizations written in that same language, such as Drupal, Wordpress, and Joomla.

Well there are quite a few languages (java, C# using ASP.NET, PHP etc) plus scripting languages (javascript, Angulas JS, Jquery etc.) that are used in web development. It would be personal choice based on which of the development language you find interesting.
By the way, web development is not just about designing flashy UI. Most of the times there is lot of background code which implements the business logic (translated from the requirements).It's important to start with the basics so html,css and javascript are pretty much necessary for understanding Web development.From there you can move into the backend .

All The best and Happy coding !

Knowing that you have the natural characteristics of a web developer is a great start, but you won’t find success with those qualities alone. In order to excel in such a technical profession, it’s imperative that you master the hard skills to compliment the soft ones.

We used real-time market intelligence from BurningGlass.com to identify the top five web technical skills employers are seeking in web developers.* This will give you an idea of which skills you should focus on sharpening to become a desirable candidate in this field.

Top 5 in-demand technical skills for web developers:
JavaScript
jQuery
HTML5
PHP
JAVA

Not familiar with some of these programming languages? Don’t worry! This is precisely the type of training and expertise you can expect to gain from earning a degree in web programming.

Since you just started your major in computer science, it's safe to say, you can easily learn how to do web development. I do web designing, mostly for clients who asked me to make their websites based on my current skills, I mainly just use HTML, CSS, PHP, and JavaScript. These are the basics and key points when creating front-end web development. From what I've seen, the most languages web developers use and write are JavaScript, Java, Angular, and JQuery. Technically, you could just create a simple web with just HTML and CSS while PHP and JavaScripts adds better functions and layouts.

As far as languages there are obviously the big three: HTML, CSS and Javascript. You need these to do any kind of basic web development. The reality is that if you want to build any seriously web applications you'll also have to spend time learning the tools that help with development workflow as well as at lest one Javascript framework. Your best bet at the moment would be React.js since it's the most popular one. Make sure you get the Javascript language basics first before you dive into a framework.

Being a web developer also means working with designers. It's a collaborative work that usually involves learning how to use an application such as Sketch or various other web based design tools such as Invision. I would recommend looking into those.

As a bonus I would keep my eye on Rust language. It's one of the newer languages that is not primarily designed for web development but it will become more relevant in the future as part of WebAssembly.

In terms of backend development: Javascript(Node.js), Ruby, PHP and perhaps Java in bigger companies.