What languages should I know to develop these kind of websites?

namecheckr.com uses PHP for back-end (Laravel which is a PHP framework).
You might want to consider getting familiar with PHP, Python or Ruby to develop web applications.

Any language you want! As long if there's a server than runs it, take your pick. When you view a page's source code, you only see what's served to you: HTML, CSS, JS. HTML lays out the page, CSS styles it, and JS modifies the DOM and negotiates transactions between the server and client. You won't see any server side code in your browser.

As far as choosing a language to develop a web app:

I have no experience with .NET but I believe it's a solid platform and very scalable.

Javascript is an extremely useful language to know. It's one of the most popular languages on Github and can be deployed both server and client side.

Working with JS can be a pain for newcomers. It's tricky to debug and is full of quirks -- it is, however, a very expressive language. JS's popularity is its strongest feature; there is a wealth of resources at your disposal -- frameworks, data storage, communities...

Then you've got databases... That's another discipline in itself. SQL is one of the most common databases on the web but you might want to look at MongoDB.

There's never a right or wrong answer. Becoming proficient in a language takes time. However, I would recommend you read: Eloquent Javascript. Don't rush it. Do all the exercises. It's a fabulous book and contains plenty of solid tuition, not just in JS, but in programming itself.

First of all you need to know how to build basic websites : HTML + CSS .
Then you need to make sure you know how to make it dynamic and reactive on front end , user interface - JS
Any server side programming language will work as you will be communicating frontend -> backend , .NET has all the tools you need, so if you fell strong with it and you like it just use your skills.
If not - python/php/ruby/node.js will work as well. PHP seems to have a bit of bad reputation, but it works and it's probably easiest to learn as a platform.

So my advice is - just try to build a minimal version/a prototype of what you want to build.
Start with simple frontend, learn the tools. See what you're missing and rebuild etc .
There is no magic pill.
If you're a programmer you should already know that nobody will help you if you don't search for solution yourself.

PHP and HTML are the basics to create this type of sites.
These are not much difficult.

That's because you're only able to see what your browser receive from the server.
You're looking a the client side of the communication, but you can't know what happened server side to obtain that code.

I think you shoul learn PHP.It's very simple and pupular

html then css then php then javascript

PHP is going to be the easiest for you to start with since it is C ported to the web.

Hi, Why don't you give Node.JS an opportunity to help you out. With Javascript, HTML, CSS, you can build a really big website. You don't even need C# and ASP.NET.

HTML and CSS are pretty much the basic languages for web development. You'll definitely need to know these to develop any kind of websites/web apps. And that is just for the front-end (what you see) part. You should also add JavaScript to that list to add more functionality to your site.

For both the websites you've mentioned, you only get to see the client side languages in the source code, that's why there's only HTML, CSS and JS.

For your website development, you should focus on HTML and CSS at first. You can try them out with website development platforms such as Blogger and WordPress (which uses PHP as well). After these, you should move on to either PHP or JavaScript. Both have been around for quite a long time, so you will find a lot of resources on the web to help you out.

PHP is heavily used for server side programming, and thanks to WordPress, it is used in a major chunk of websites all over the web.

JavaScript may seem like tough to start with, but you'd need to know it in order to add functionality to your website, and it can be used on the server side thanks to Node.js, which can take out PHP any time in raw performance.

There are other options like Python and Ruby for back end as well. But I believe it is worth to give JS a chance, since it is applicable on both client and server side along with the high performance output when compared (especially to) PHP. This blog post should definitely help you out
Node.js Vs PHP | Performance Comparison - Node js or PHP

You also have databases to take care of. A number of options are available, MySQL being the most popular choice and well-suited for PHP, Python. But if you do go for Node.js you should pick MongoDB, which will work better since both are event-driven.

Good Luck.