To connect to Lnet, you need a computer or a router with a regular local area network (Ethernet) connection. The device must be configured to use dynamic network configuration (DHCP), which is the same as in most networks, so you'll usually have it enabled. If this is not the case see e.g. Microsoft's guide for changing the network settings on Windows.
In addition to the computer or router, you'll need a LAN cable with the 8-pin "RJ45" connectors. Note: don't try to use cables with the smaller four-wire "RJ11" connectors meant for landline/DSL connections. The connection will not work, and the smaller connector may damage the connector in the wall socket.
In most properties connected to Lnet, all cables within the apartment are connected to the network, but at least in Laserkatu 1 (Timppa), you need to check the active socket in the box near the entrance to the apartment. In Laserkatu 3, there are two sets of network sockets. Only the ones installed in cable ducts on the walls are in use, the old connectors near the landline socket and cabled within the wall are not in use.