You'll notice on the "Addressing and VLANs" page that once you enable VLANs, a new link will appear to "Add a local VLAN" so you can add your 8 VLANs and save that. The MX will take care of all the interVLAN routing and all of the DHCP service by default for every VLAN. By default all of the LAN ports will be trunk ports with native VLAN 1 and all VLANs allowed. Then as Adam pointed out, connect up your switches, and by default the switch ports should all be trunk ports with native VLAN 1 which basically makes it plug and play.
Then, if needed, you can configure individual switch ports as access ports in a specific VLAN, or as trunk ports but only with your 8 specific VLANs allowed, etc. You can also, if needed, to per-port VLAN configuration on the MX.
More info
https://documentation.meraki.com/MX-Z/Networks_and_Routing/Addressing_and_VLANs
and
https://documentation.meraki.com/MS/Port_and_VLAN_Configuration/Switch_Ports