When you connect via Firewire you don't generally see anything happen. It won't show up as a drive under "My Computer" like say a USB device. But a video editing application should see it when you invoke the video capture function.
What OS are you running? If XP or Vista, you could try Windows Movie Maker and see if that works.
Mark , My experience is rather different in that: Ill link some screen shots I made while typing this post in a minute
SCREENGRAB HERE
If you can ignore the suspect PQ,(

) You'll notice the dialogue above, and the inclusion on a Sony DV device next to the scanner as a "device" in the " My Computer" window at the bottom after connecting up the camcorder via fire wire
In general, ( although not invariably) , when you connect up a camcorder to a PC running windows XP, there would be a "ping" notification sound ( such as you have with USB devices) and a dialogue to ask what you want to do with it
The video transfer never happens without prompting and there has to be software which mainly ( though not always) can control the camcorder transport
The above scenario is typical on all my systems, this may not be the case all systems
Saying that, if (it should, but) doesn't happen, it may not be your fault
There are 4 components that effect smooth transfer
The camcorder ( and its firewire port)
The firewire cable
The PCs firewire port
Windows
If any of these isn't right , you wont get to "see" the camcorder
Tracing the problem is simply one of elimination
Some camcorders have the ability to enable or disable firewire transfer in the menu: This needs to be enabled if so. Some Firewire out is only enabled in Playback ( Possible : although some are enable whichever mode camcorder is in)
Windows Movie Maker (if installed) would usually prompt you to use it enable transfer even if you have no other software installed that can
Another one you can try is
WinDV: free and easy to use