Depends on whether they have software installed to do that or not.
But if they don't, but have a decent router/firewall then it's easy enough to pull up real-time logs which devices are connected to which IP addresses. From there, it's a simple matter of finding out what the remote IP address belongs to.
That's more trouble than it's worth, though. If they wanted to monitor you, they'd just buy software that lets them do it. And the fact that they're monitoring you or have the right to do so, would be included in your employee contract.

More than likely no there is no IP tracking software on your PC (which is the front line for most IT guys, save for FBD ^ up there who knows more than 80% of em), but make sure you have your browser set to delete your history when you close out, and clean out your temp files (cookies and crap like that) regularly. A good way to keep everything on a beginners clean slate at the very least.

Yea, I'm the sysadmin at our company and it's a pretty small shop. I don't monitor anyone. Mostly because it's not in the employee terms. If I were told to, though, I have the functionality right on my router. Or I could buy an intermediary device behind the router and do tracking/blocking.

216,

I'd refer to the employee contract/terms and see if it says anything in there. If not, there's probably no monitoring because it's not a mandated practice, therefore no resources would have been put toward such a practice. But like Plank said, it's probably a good idea to clear temp files if you don't want the IT guy finding your dirty laundry should he need to diagnose some issue on your PC and find himself wading through stuff you don't want him wading through.

Here's a cool trick:

Create a folder on the desktop and name it "God Mode.{ED7BA470-8E54-465E-825C-99712043E01C}" (no quotes) The folder wil change to look similar to the control panel icon and will give you all of the controls in one place.

You could name it anything you want instead of God Mode, but God Mode is pretty freakin sweet.

Yea, I remember doing that a while back, but then realizing everything in one folder was just way too much crap to sort through. I just use the start search bar.

I hear ya, but a lot of times I forget what things are called, so this helps in that aspect.

I'm planning on building my own gaming desktop pretty soon, so I'll be consulting this thread.

You should check one of those sites that have the checklists to go with certain budgets so you know they will all be compatibile especially if it is your first time building.

I've done a little bit of that, but my brain is a little rusty on piecing it all together. I know the general specs I want for certain components (CPU, RAM, etc), but I get lost sometimes trying to piece it all together, such as making sure the CPU socket is correct, as well the VGA slot, among other things.

PCPartPicker.com

If there's compatibility problems the website will tell you.