There are multiple solutions to this problem. The "most elegant" one is relatively wasteful, but very common, and uses 9 IP addresses to do it. This is the way most professional ISPs would handle it.
You get an IP address for your router (same as most regular accounts) - this IP address is associated with the WAN Interface of your router. [ You could use an RFC1918 IP here if agreed with your ISP, but this probably stuffs things up for their neat systems]
You then ask your ISP for a "/29". This means you are asking for a block of 8 IP addresses, (including the 2 unuseable ones associated with the routing protocol - Simplifying a bit - the first and last IP address of a block is considered to be "unuseable"). The ISP then routes these IP addresses down to your router as a single block. They like doing this because it simplifies their accounting and routing table, and is very standard.
You then further divide this block of 8 IP's into 2 blocks of 4 IP's. This gives you 2 blocks of 2 useable addresses. You bind 1 of the 2 usable addresses to each interface / vlan on your router and provide the other IP address to the client.
Thus you might have something which looks as follows:
ISP (18.104.22.168) -----> (22.214.171.124) router (126.96.36.199) ------ 188.8.131.52 (PC on network 1)
+-- (184.108.40.206) ----- 220.127.116.11 (PC on network 2)
In the example above, the ISP has assigned your router 18.104.22.168. Your router [ which
needs 3 interfaces/virtual interfaces ] has the default network configured to point back
to 22.214.171.124, so unknown traffic goes to your ISP.
On the router
The first LAN port is configured as 126.96.36.199 with a netmask of 255.255.255.252
The second LAN port is configured as 188.8.131.52 with a netmask of 255.255.255.252
The first PC is configured with an ip of 184.108.40.206, a netmask of 255.255.255.252 and a
default gateway of 220.127.116.11
The second PC is configured with an ip of 18.104.22.168, a netmask of 255.255.255.252 and a
default gateway of 22.214.171.124
IP's 126.96.36.199 and 188.8.131.52 are called "Network" IP's and are not used for traffic.
IP's 184.108.40.206 and 220.127.116.11 are called "Broadcast" IP's and are not used for traffic.
The router requires 2 IP's on the LAN interface.
An alternative, similar but less elegant method would be to get your ISP to route a /30 across your connection - this requires a total of 5 IPs for your network, and 2 are wasted. You would need to use private IPs (like 192.168.1.x) for each of your LAN interfaces and then use NAT to translate these to real world providers.
FOR THOSE WHO WANT TO SHOOT ME DOWN FOR THE USE OF IPS - CHECK WITH YOUR NETWORK PROFESSIONAL FIRST - MOST "point to point" connections are configured using 4 IPs as I've
made extensive use of above.