If you want a top level domain such as .com or .net, you would need to pay for it.
You can get a subdomain with Weebly such as the following:
test.weebly.com
There are many different ones online. Some are free and some you have to buy a domain. Weebly and Webs are good, free domain creators. It depends on what you are looking for. There are 1,000s to choose from.
On the homepage when you have just logged in it should have a bit that says "Account Type: Free". It will show this if you have not yet upgraded to Weebly Pro. Next to that it should have 2 buttons- "Uprgrade to Weebly Pro" and "Get Weebly Pro for free". Click on "Get Weebly Pro for free" and just follow the instructions! Simples :D
You can register a free domain name by going to any one of a number of websites that provide registration for free domain names. They will guide you through the process of registering your domain name.
Weebly is a free website builder service that shows you how to build a website from scratch in a few simple steps. Popular opinion suggests that Weebly is a good service.
Here's the list: Blogger by Google, Weebly, Squarespace...Also, you can start your own website, you've got the domain name, now you only need to find a web hosting company.
You can use: www.dot.tk . Here you get a domain like: www.mywebsite.tk for free.
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To check for a domain is free of charge. This is free with all the domain services, you will need to make sure that the name you decide on is not taken and this can take up to a couple of trys. There is no fee until you have picked out a name.
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There is no way to get a domain name for free. Domains need to be purchased from an official provider such as GoDaddy in order to have storage space online.
It's not possible to get a free domain name with .com domain name. But you can search for some other sub domains or .cc, .pk domain name.
Owlient coded Howrse themselves, and most likely purchased their own servers to host their domain. They did not use a free host (such as Webs, Weebly, or uCoz) to create their website.