How route 1 vlans internet traffic through a proxy on another vlan?

Could someone, as if they were speaking to a child, explain the steps and infrastructure I would need to accomplish this:

I have a Fortigate 60e firewall.

I have been tasked with setting up a network with 4 VLANs with different subnets. VLAN1 contains a proxy server and there is to be no internet access except through this proxy for both VLAN1 AND VLAN2. VLAN 3 and 4 I can control normally with the 60e policies. 

So far I am thinking, create 4 vlans in the 60e.

Vlan 3 and 4 are fine to deal with normally.

Now I just don't understand networking enough to know what to do from here.

How do I set up a proxy on VLAN 1 (squid?) and then how do I get traffic from vlan2's subnet going over to vlan1's subnet and going through the proxy? How does that work?

Gateways, switches, broadcast domains, multiple subnets???

Could someone please give me a little guidance here?

I feel out of my depth here so thanks for any help guys :)

Jono