So back to the original problem, here's what I'd do...
I'm making the assumption that this is a small, non-union company.
First I'd ask myself what I think about the work this particular employee is doing. If they're doing all the work that's asked of them, doing it on time, and doing it well, then I'd probably say, "whatever," and get on with more important things. Some people work more efficiently than others and I'm not going to punish someone for surfing the net if they're getting their work done in an acceptable manner. Don't micro-manage. Employees hate it.
Second, if the employee is not meeting my expectations, I'd sit them down and talk about it with them. Clearly tell them what the expectations are and how to meet them. Ask if they need help meeting them. Maybe the employee doesn't even realize they're supposed to be doing something they're not. Maybe they don't realize they're not supposed to be surfing the net. Maybe they don't realize it's pissing you off. Who knows? You won't unless you have the conversation.
Once you've told them your expectations, monitor them as you normally would. If the behaviour isn't changing, I'd probably give a formal warning and record it on their file (if they even have a file).
If the behaviour still persists, and my original assumption is true, I'd turf their ass. If it's a short service employee, they'd only get a couple weeks notice anyways so I'd either pay it or if they really pissed me off I'd make them sue me just to aggravate them.
If this is a long service employee or if I'm potentially vulnerable to a Human Rights complaint (the employee is a woman, disabled, visible minority, etc.), I'd tread more carefully and would likely turf them with notice. And I'd make the bastard work the notice period. Mwah-ha-ha!
If this was a union job or a bigger company, I would take a very different approach.
