HOW CAN WE GET FREE .COM CUSTOM DOMAIN . HERE IS THE TRICK.

There are many ways avaible through which u can get a custom domain. 

And it mainly depends on the property for which custom domain u need 

Here are the ways by which u can get custom domain for freee.

Domain Name - At HOST MY WEBSITE  you will get free subdomain. But if you want your own domain.you need to  may either have to purchase it or you can go for paid hosting plans for which in which you will get free domain name for life.

Below are a few methods,

• You can a s wells as a static website using GitHub Pages and use a custom domain name of yor own.
• You can even sign up for Amazon Elastic Compute Cloud (Amazon EC2)and create a micro instance for free and you can build a Rails or Node app or even a static file server and use a custom domain.
• Try the or Heroku | Cloud Application Platformand host a free Rails app or node.js app. And you can use a custom domain name there as well.

Domain names are not free. You can get a domain from GoDaddy.com or BigRock.comor some other domain for a small fee 

If you don't want to pay for the domain and want to create a free blog, you can always use WordPress.comor Blogspot.com They will give you a subdomain. But in your question you have mentioned that you want a custom domain, so you might have to pay a small amount.