Brian's right -- think of it as the *forcing* more air/fuel into the intake than would be normally possible. The turbo "force feeds" the engine -- stuffs more into it -- and thus causes it to produce more power.
The turbo mechanism is actually two "fans" (or blower impellers) connected by a single shaft. On the exhaust side, the impeller is driven by the exhaust gases after they have left the cylinder and are on their way to the tail pipe. They spin the fan very quickly. The shaft therefore turns just as quickly on the other end. The "fan" (or impeller) on that end is located in the intake side, downstream of the carbuerator. This fan is therefore taking air/fuel and compressing it into the intake manifold. That's how a turbo force-feeds the cylinders.
Really, they don't WANT heat to be transfered from the exhaust into the intake. Preferably the intake mixture would remain fairly cool, because the charge is denser and that carries more power than a hot mixture. Some later turbo engines (not Pontiac) have "intercoolers" to help cool down this compressed intake charge and thus give better power.
The turbo "fans" and shaft spin at pretty high speeds, which is why it's important to keep them oiled and maintained by changing your oil at regular intervals.
So....that's the basics of turbo engine operation. There are other aspects, like "waste gates" and such, but those are just variations and/or options on the basic turbo operation.
Rather than lose you in all of that, I'll just see if you have any questions about this idea so far...it's best to have a firm understanding of the process before we start branching out to other aspects of how it works.