In the new window that shows all available wireless networks, find the name of the hotel's wireless network. You can usually find this information, as well as any passwords needed to connect, in the hotel's guidebook in your room.
In this example, hhonors (for Hilton Honors) is the name of the network, and, as you can see, it's an unsecured network.
Click on the wireless network (Mac) and, on Windows, click the "Connect" button to connect.
Depending on your hotel's network setup, you may be prompted to enter the security passphrase to connect. You can usually find this information, again, in the hotel guidebook.
By the way, another way to get to the list of available networks (e.g., if you can't find the wireless network icon) is by going to your control panel, then the network connections section. Right-click on Wireless Network Connection and choose to "View Available Wireless Networks".
If you're having trouble finding the right wireless network name on the list of available connections, see this tip on manually adding a wireless network or joining another network (for Macs). However, chances are if the network isn't visible--and especially if you don't see any wireless networks there, there's something wrong. Time for some wireless network troubleshooting or you can call your hotel's help desk.