The IP address of a device can be set one of 2 ways; manually or automatically. When you set the address manually (also referred to as static) you simply go into the adapter properties and type in an address. If the address you enter is valid for your setup it will work. If not, then it won't. The alternative is the address is set automatically via DHCP (dynamic host configuration protocol). For DHCP to work you need a client (your device) that asks for an address and a server (your modem or router or ??) that gives out a valid address.
Often when you have a true modem (a device that translates one protocol to another) you will have a single input (telephone, fiber, coax or other) and a single output (Ethernet). Devices like this have only 1 IP address and thus can only support one device (computer, phone, tablet, etc). If you want to use multiple devices, then you will need a device that will translate the single address to multiple (NAT). These are often called residential routers or gateways.
The way you describe your network is a bit confusing. Please describe all the hardware you are using and what device this LAN port is on. Model numbers of your devices would help. Thx.