This probably needs more editing and, is certainly missing things but, I’m out of time to work on it for now. I am pretty sure there are a nearly infinite number of articles covering this topic online.
In the interest of full disclosure: my company (Evermore Enterprises) provides web development and hosting services. We are not the in the low-price market. We provide managed hosting (where we take care of keeping your site secured, software updated, etc.). We often rescue businesses from free and inexpensive services where they are having problems with getting hacked regularly, can’t get support, etc.
If your website is a core part of making your living, please consider getting professional assistance from someone who knows what they are doing.
None of this should be taken as an endorsement of any particular service:
A lot of people will have some web hosting service they may not even be aware of. For example, my ISP includes static hosting of a few MB with my service.
Some registrars include some hosting service with a domain name registration or, for a small additional fee. Some of those include tools to automatically install something like Wordpress (see below). That is probably going to be your optimal free/cheap option.
You can also get software that will let you put together a static site visually. RapidWeaver and Sparkle come to mind. Those both show up in bargain software bundles regularly.
Wordpress is the most popular content management system for building websites. The software is an open community project. Wordpress is very adaptable with plugins to make it do all kinds of specialized things. You can build a very serviceable website with a default installation and one of the stock themes. Most providers that offer Wordpress hosting will set it up for you.
Because the software is open, it is easy to extract your Wordpress site from any given provider and, move it somewhere else. This is useful if you start having problems with the provider or, if you grow beyond the services they provide.
In theory, You can get a free Wordpress site from http://wordpress.com – it does not appear to be working at the time I am writing this, though. A number of other providers offer Wordpress sites. Some are free (possibly with imposed advertising, usually with limits to what additional components you can install). Here is a fairly current list of some I found:
Some providers will set you up with a Wordpress site on a shared server for free or for a minimal cost with a domain name registration. For example:
I have seen offers around $7/year from some registrars.
There are a bunch of companies now providing web-based systems that let you make a website using visual tools. Some of them have free levels of service, like Wix, Weebly, Webnode and Mozello. Those usually run ads on your pages in exchange.
Paid services like these include SquareSpace, JimDo, Duda, One.com, Virb and more.
One of my key issues with any of those, free or paid (but especially paid), is that the site is tied to the provider. If you have a disagreement with SquareSpace, you can’t pick up your site and go somewhere else.
If you have a GMail account, you can create a simple website with Google Sites. This is still a proprietary website-as-a-service but, it’s Google.
It used to be possible to host static sites directly on Dropbox but, they shut that down. There are, however, free services that can connect to a Dropbox account and provide the hosting portion, like:
Google Drive and Microsoft OneDrive
Similarly, there are services that provide front-ends to do the same thing with other file hosting services:
If you are looking to run a web store, there are a number of other options.
Some payment processors, notably Square, will let you set up an online shop with their system for free, if you use them for payment processing:
Etsy is a popular online marketplace that charges a minimal fee for each catalog item and, a percentage of each sale. Additionally, people know Etsy as an online marketplace for handmade items. So, you get some extra traffic from random searches and their other promotion built in.
What else am I missing? Everybody feel free to chime in.