I suspect handsfree is in fact a myth, as most phones need a basic on / off type command to start / end the call.
There are cheap ones which rely on the phone's mic and speaker. They just clip to a dashboard, but probably won't be that effective bringing in lots of background noise.
A slight step up, is the long lead from the phone to an earpiece and mic. These aren't really "handsfree" as you can't use voice commands for dialling.
At the other end, will be professionally installed kits that holster your phone, use the cars radio speakers (cutting off the radio when phoning) with a mic routed somewhere like the mirror. Activation may be by voice command or press of a single answer / cancel button.
The mid range options usually rely on bluetooth. These are the clip on earpieces, or alternatively you can get standalone speaker / mic units that clip onto the sunvisor. Some in car navigation systems also double up as bluetooth units.
To answer a call simply single press a button on the bluetooth unit, then talk away. Call ends by repressing of the button or the other end hanging up. To make a call, assuming voice dialling has been set up (i,e, assign a voice command of "office" to your work number in the address book), simply press the call button on the handsfree thingy and speak the name.
Personaly I find the sun visor thing great. It isn't intrusive, and mine has great battery life of a couple of weeks usage before recharging. Callers have no problems hearing me, and it can be moved from car to car. Best of all the phone stays in my pocket. Downside is you can't see texts
The earpiece type things I just find uncomfortable.