This isn't AWS with 20 years of experience, but for how new they are, they're doing things extremely well, I have been using this hosting for about 2 years now.

Steps to add a custom domain:

1 - Go to your project/service, the one you wanna publish, section Networking

2 - Select the + Custom Domain, and fill the info:

3 - Click the Add Domain and you will have this:

4 - Copy the value, and go to your domain provider... from now on you are not working on railway, all railway configuration is done at this point.

I'm using Cloudflare, but you can use anyone you want, as long they allow CNAME

5 - Add the info as a CNAME:

ALL DONE

After this, you can go to your super-magic-domain.you-domain.com and the 'traffic will be redirected to' you service

Note that you will need to wait for dns propagation (Clodflare takes like 3 sec, but still)

That's all

Feel free to let us know if you have any question

@root101 gave a very detailed reply do not want to steal the bounty from them but hobby is limited to 2 domains per service I do not know about free

I am linking the documentation as it may help https://docs.railway.com/guides/public-networking#custom-domains