I have two vlans setup currently. One vlan is the main vlan for the
entire site. It's ID is 1 and then I have a vlan setup for guest access
through the wireless system. It's ID is 10.

On my core switch (which is a netgear layer three switch) port 47 is
connected to my firewall which is set to act as a DHCP server, DNS
server, and gateway for the internet. The idea being that when a guest
connects to the guest SSID they will only have access to the internet
and nothing else in the building.

Here's part of the problem (excluding the fact that my knowledge of
vlans is sorely lacking). When port 47 is connected to the firewall
random computers on my network will be assigned an IP address from it.
My switch shows that vlan id 1 has all ports mapped and marked as 'U'
for untagged. vlan 10 (guest vlan) shows nothing tagged. I'm a
guessing this is the start of my problem. i'm just not sure what to do.

Anybody got some help for me?