There are different ways of doing it. The basic step here is that you need to buy a domain name of your choice. There are free domains available with extensions of popular blogging platforms (Eg: yourdomain.wordpress.com). If you like to get a professional website, you need to buy a domain name.
Once you have purchased the domain, you need to host it. There are several free as well as paid hosting platforms available online. You can select this based on your budget. (I am using Hostgator for my paid hosting blogs and 000webhost.com for my free hosting blogs).
Site design is the next thing you need to focus. You can build your site in the professional way with the help of a web developer. If you have budget constraints, I recommend you to install a blogging tool like wordpress in your domain. (There are several youtube videos and informational sites to help you with this process). You can use a theme of your choice and start uploading content, images and videos in your site.