It's a pretty straight-forward process, non-trivial, but not complicated and easy to implement. You just need a few modest resources in order to accomplish this. Namely:
The step by step details, of which the first three items above, are here:
You'll need to decide how and where you want your website to reside, and either hire a designer/developer or simply do it yourself with a static site or use some CMS like Drupal or WordPress.
You can run each of these on inexpensive virtual machines, with most of the hardware specs being in the neighborhood of 2 to 16GBytes RAM, 2 to 8 Xeon cores, and not much storage. For more precise hardware requirements to begin with you can see the official recommendations here:
The operational cost for this machinery varies widely, but if you check over at LEB and other market resources you should be able to launch a reliable platform for under $30/month for each of those machines.... and much less if you hunt around, although I generally hesitate to recommend OpenVZ, instead suggesting you choose KVM, Xen, or VMware for your virtualization - this is much cheaper than Google Compute or AWS by far.
These are by far some of the most clear, simple to follow, and concise docs leading you towards your goal.
I recommend using Slackware -current, Arch, Gentoo, or Debian -testing, as your base OS - these are all tried and true rolling distros that won't find you in a bind in a couple of years as they continually upgrade to the most current versions off software while you're in production; not to mention the reputation of these distros for providing a rock solid foundation for operational stability, since you're going to need to ensure that your servers NEVER go down.
Good luck and enjoy!