Go to
https://lowendbox.com/ and choose the cheapest Linux VPS server near your country, with 512 MB RAM, other parameters do not matter. It should cost no more than $2 per month, bit you can find offers as low as $1/month. Do not buy Amazon AWS or Google Cloud or whatever Miscosoft is offering, they are way too expensive, aim for small unknown cloud hosting companies.
Pay for one month, then choose the latest Ubuntu or Debian as your distribution. 70% of all Linux installation manuals on internet are about Uhintu, this will make your life easier.
Start your server in the web control panel of your cloud hosting.
Install SSH client to your PC, log into your server as described in the web control panel, then run these commmands
sudo apt-get install openttd cron nano
Enter your server password, then 'y' when prompted.
This will likely install a slightly old version of OpenTTD, look which version is written in the command output, and download the same version of OpenTTD to your PC, they need to match.
Now run
openttd -D
That's all, you are running your own dedicated server. Launch OpenTTD on your PC and search for it in the server list.
Now close OpenTTD, press Ctrl-C to stop the server, and run command
crontab -e
When you are asked which text editor to use, choose Nano and absolutely do not, I repeat, never choose vi. If you launch vi by mistake, you will have to abandon this VPS and buy another server (and I am only half-joking)
Now, create a new line that looks like this
@reboot /usr/bin/openttd -D
Save the file with Ctrl-S, exit Nano with Ctrl-X, then reboot your VPS in the web panel. Your dedicated OpenTTD server will now launch when VPS reboots. Which may happen at random, because your cloud hosting is the cheapest, but let it not bother you.
I will leave instructions about editing your server config file for later.