How to give computer URL to access over the internet?

You need to go a domain registar, and register a domain name with them. You then create an A record to point to your IP address with whomever is hosing the DNS servers that are hosting your domain (this may or may not be your registar) - after that, simply use the domain name in place of wherever you'd use the IP address.

Some websites, like DynDNS, do half the work for you. They have already registered a domain and set up the DNS servers, and then hand out subdomains. You can't get example.org with them, but you can get example.dyndns.org to point to your IP address for free (the other way costs about $10/year depending on the type of domain name you go with). All you have to do is sign up at the website and pick a subdomain name and enter your IP to get started :)

You could sign up for DynDns: http://dyn.com/dns/

That's how I've done ssh to my machine in the past. I believe they have a free version that allows you to have at least one domain name.

It's particularly nice because of the features they add such as the "Internet Guide" which allows for some content restriction control.

If you have a static IP, you can assign an alias for your ip in the /etc/hosts file:

127.0.0.1 localhost
xx.xx.xx.xx alias.whatever

If you have a dynamic IP, you could use the service by sites like http://www.no-ip.com/ to get a subdomain.