Today in my work the people from security are going to block internet access and only admit enterprise local pages. Luckily, there is a free Wi-Fi connection which I have access from my Motorola Milestone. Is there any way for me to tether the Wi-Fi connection over USB to my computer?
You can do this using PdaNet.
Assuming your computer doesn't have a Wi-Fi card already and you're not rooted, I would probably just buy a USB Wi-Fi card. You can almost certainly buy one for less than the cost of PDANet.
If you are rooted, Cyanogenmod has had built-in tethering in the Wireless & network settings menu for a while now. You can enable USB tethering and connect your phone to the hotspot to essentially have it act like a USB Wi-Fi card.
For my other tethering needs that aren't covered ROM-covered (e.g. Bluetooth network tethering) I've preferred Android Wi-Fi Tether, which is free, although I don't know how well it works on the Milestone.