By default SQL Server instances don't listen for TCP/IP connections, so verify that this is enabled:
Also you need to make sure that firewalls between your client and the server are not blocking the connection. For the default instance under standard configuration TCP port 1433 needs to be open. If you have multiple instances then things get more complicated. See https://msdn.microsoft.com/en-us/library/cc646023.aspx for more details.
These are the most common cuases of complete failure to connect to a remote server. If all this is configured correctly then, as Tom V suggests, we need more information in order to be able to help.
Warning: It is strongly recommended that you do not open your SQL server ports to the Internet at large. If you allow connections in from the outside network then make sure you limit it to specific source IP addresses. If you can not do this because the source address(es) are variable (for example if you need to connect from a laptop that moves between networks a lot) then consider instead setting up a VPN to allow access through the firewall that way instead of directly. Even for a single fixed source address, I would still tend to prefer the VPN option.