To transfer different VLANs over the same physical network link, they have to be marked somehow, or you wouldn’t know which packet belongs to which VLAN. This is what VLAN Tagging (802.11q) does: It extends the header of IP packets to include the VLAN ID.
Inside your switch, VLANs are just a way of joining ports together to form a “virtual switch” of sorts. If you want a port to be attached to multiple VLANs, you have to use VLAN Tagging.
The challenge in all this is how to handle these tagged packets. Windows, for example, is very poor at VLANs. And when it comes to SOHO routers, you’re mostly SOL. Unless using an aftermarket firmware like OpenWrt or DD-WRT, that is. If a device is not VLAN aware (or not configured), it’ll most likely drop the packet because of bogus content.
So now that you know how to set up your switch, it’s time to move to your internet gateway device. I strongly suggest you open another question for that purpose.