There is plenty of cloud servers providers, DigitalOcean, linode, aws amazon to name a few. They also provide instructions how to set up the server (configure ssh access and stuff). Search for it on the google.

Having that, go and register a domain, e.g. example.com and point it to your previously setup server's IP address. Every domain registar have tutorial how to do that.

From the odoo website you'll have to take tutorial how to set up odoo and have it run on the server. This will leave you with working odoo instance accessible using your registered domain with port appendix, e.g. example.com:8069

If you want to get rid off the port part of the url, and type only example.com to access the odoo go and use reverse proxy for that, e.g. nginx - after configured when it receives request from example.com it will redirect the request to example.com:8069 without showing the port for the user.

As Yenthe stated it is quite complex setup and every single step depended very heavily on solution/tech/provided you've chosen, so the general answer is quite short, while detailed one will be hell long.

Should you have any question I'll be happy to help further.