If I build my own network would I have to have a DHCP Server in every subnet?

It is my understanding that when a client tries to obtain an IP address from a DHCP server it sends out a broadcast message to find the DHCP Server.

I intend to build a network with 2 switches, a vlan on each switch, with a router between them. Would I have to have two DHCP servers?

Switches will forward broadcasts, but routers will not. How can I have 1 DHCP Server for both vlans?

This must be a common issue. I cannot see companies in enterprise environments spending that much money on servers.