Just installed Windows 7... Need some help getting Wi-fi?

I just installed Windows 7 Ultimate 32-bit on my IBM ThinkPad T42, and I have no idea how to connect to Wi-fi hotspots. I know that the computer is indeed capable of connecting to a hotspot, as I had Windows XP professional prior to Windows 7 (which came with the computer) and I could connect. The internet options on my computer are only Broadband and dial-up. I didn't think anyone used dial up anymore and I don't even know what 'Broadband' means. The unsecured wireless hotspot I used before with Windows XP I don't think even belongs to us. There is absolutely NO way to connect my computer to the internet right now (I am writing this on a Mac which uses the same wi-fi network I want to connect my ThinkPad to). I have literally no idea how to do anything with 'drivers' or whatever those are. So would anybody be so kind as to post idiot friendly step by step instructions on how to get wi-fi on my computer? Also, when I try to turn on my wi-fi with the hardware switch (which is actually just the keyboard command "Fn+F5") Nothing happens, the indicator light stays off, no lights come on, no indication of anything. Anybody have any idea?