It sounds like you may want to do some reading-up on how VLANs work (http://en.wikipedia.org/wiki/Virtual%5FLAN for starts) to get a better understanding of what you're trying to do. When you get into running the PCs and phones on the same cable drop your problem becomes a bit more complex (but still highly feasible).
The routers and servers for each "side" of the network would be attached to "untagged member" ports of the VLAN to which they belong. Untagged ports are really easy to understand-- they're basically like breaking an Ethernet switch into multiple virtual switches, each isolated from the other.
As you've stated, many IP phones have built-in Ethernet switches for connecting at PC to the phone. The phone connects back to the wiring closet Ethernet switch. The wiring closet switch-port the phone is connected to may have a "voice VLAN" configured, or may be configured as a "VLAN trunk" port with membership in both the "PC" and "voice" VLANs. Typically, the phone handles tagging Ethernet frames coming from the PC so that the switch "sees" the PC as being a member of the proper VLAN. This is typically negotiated between the closet switch and the phone, but some configuration is usually required. I don't know of a switch that's set-up with a voice VLAN "out of the box".
This configuration varies from phone-to-phone and switch-to-switch. Without knowing more about your infrastructure I can't give you any step-by-step directions.
You may want to think about getting somebody to come on-site and help you with the initial configuration. Getting this right from the beginning will give your users the most consistent and reliable pexperience. Starting a new deployment, particularly something sensitive to poor network conditions like VoIP, on a sour note can really hurt user perception.