That really depends on the organization and how critical it is for applications to remain up and running, and lastly, what type of circuit services are available between sites. If you can stand some downtime, then cold or warm sites work. If it is a more critical operation (hospital, manufacturing, etc.) then a hot site will work better.
To set up either one, you will need to work with your carrier. If you have a dedicated line or at least a simulated dedicated (mapped) line you can keep the networks on the same segment if you have enough addresses. This can get tricky depending on your carrier, router, capabilities, etc. Testing can be as simple as scheduling downtime and turning one site off to be sure the other comes up. This is a critical step and should never be skipped. If you put them in separate domains, you will need to add ODBC and other mappings to both domains. You are generally better with one. But again this depends on how your router will handle the failover; the same goes for switches and, of course, workstations.
I would suggest spending the money to get someone that is authorized in your gear or get guidance from the service department of your service provider in this. Also, don’t become overly redundant. One mistake companies make is to have all servers dual mapped when in fact not all need to be. Some will no doubt be able to stand some downtime. There is no reason to spend extra money on switch ports, network cards, etc. for servers that can stand some minimal downtime (for instance a manual cutover).