There are three types of networking switching devices - hubs (dumb and not common, anymore), switches (which do not change IP addresses but also do not allow addressing a device directly) (although there are more varieties that do) and routers (which can and by default do change the IP address).
Local IP addresses can be provided by the router the computer is attached to, or manually assigned.
Knowing the manufacturer and model of the device would be useful. What is the webpage for specifications on the device.
What is the structure of your network - internet access device - global IP address - routers on the network - local IP address range - device providing wireless access ...
Your question is vast and lacking specifics. you can find your global IP address at http://whatismyipaddress.com
You can find your local IP address range by looking at your router(s) setup or looking at Network properties for a couple of computers.
To the main point, what is the IP address of the laptop and what is the IP address of the server.
Connecting a Server to a Switch is usually not recommended.