New GS308 switch will not give internet and assigns a weird ip. is this for internet or just network

> A weird IP is a totaly uncaracteristic of an ip address.

   What's the number?  Or do you just enjoy creating information-free,
vague descriptions?

> The cable moden to the wifi routher with 4 ports then one
> cable(pecfectly working cable) to the switch.

   If that means that you connected one of the router LAN ports to one
of the switch ports, then that should be right.

> [...] the switch doesn't have any mark I've tried on the 1 port [...]

   How can you identify the "1 port" if "the switch doesn't have any
mark"?  In all the pictures I can find, the ports are labeled 1-8.

> Are there interesting LEDs associated with any of the Ethernet ports
> on these devices?

   Still wondering.  The GS308 picture which I saw showed some LED
indicators.

> i need to connect more things not to each other but to the internet.

   If you connect them (properly) to the router, then you'll be
connecting them to each other and to the Internet.  A network switch is
the way to expand the router's available LAN ports.  You need a working
switch and good cables.  As you've noted, all the switch ports are
equivalent, so it's not easy to foul up the switch connections.