Firstly, I am not sure it is wise to put sharepoint available for anyone (and it will be) on the Internet.
However, to make any service available on the Internet, you will need to map the Internet side (public) IP address and TCP port to the inside (private) IP address and port. This is because your internal network will use private IP addresses that are not directly acessible on the Internet (10.x.x.x or 172.16.x.x or 192.168.x.x addresses). This process is known as network address translation (NAT).
If you already have services hosted, that can be accessed from the Internet, have a look at the router or firewall configuration, and you can probably just map a different TCP port, to the sharepoint server, and access it using the Internet IP address and this port. Without knowing the make of the router, or more details, it is a bit difficult to advise further.
Please note my first comment, I am sure that someone else on here can advise about the safety of making sharepoint accessible on the Internet, but if it is OK, then doing it is not too difficult.
A much safer method will be to configure a VPN access to the network, then only you (or selected colleagues) can access any of the inside network resources, in a very secure manner. Dependant on the firewall, or router, this is also usually fairly easy to configure.
Post the details of the router, and the config, but do remove any passwords, and change the IP addresses first. Then we can help you further.