There is not enough info given to give more than a generic answer.
Whatever an internet connection is, it requires the compatible hardware in the computer to hook it up to.Example, a dial-up connection through a phone line needs a modem in (or attached externally to) the computer to hook the phone line to. A wireless internet connection requires a wireless adapter in (or attached to) the computer.
There are different kinds of wireless adapters. The desktop might have an empty PCI slot that you could install a wireless PCI adapter card into. Or it might have a free USB port that you could hook a wireless USB adapter to. Same for a notebook, different options available.
Any time you add a piece of hardware to a computer, it has to be capable of supporting that hardware. If you're running Windows 95 and the hardware you bought only works with Windows 98 or newer, then it won't work. If you have a 200 watt power supply that is already stressed to provide enough power for everthing in the computer, and you add something else, it won't work.
We don't know the models of your computers or what OS they are running. We don't know what other hardware or software has been added to them, or if there are even any free places to hook an adapter to. We don't know what kind of "wireless" you are trying to hook up to. What hardware/software it uses. See the problem here? No one can say "Yes, go by this and this and you'll be all set."
After you get a wireless adapter installed, it has to be configured to connect to the available wireless network, which is another issue.
You have to decide if you want to know how to do this or if you just want to get online, and you're not interested in how it works. You can either sit down, and do a lot of research, or you can get a friend who already knows how, to set it all up for you.
If you want to learn, write down the makes and models of the computers and the existing wireless hardware being used. Go to your computer manufacturer's website and learn about your model. Go to the wireless internet providers website. Go to the website of the manufacturer of the existing wireless hardware. Use Google to learn about wireless adapters and wireless networking. Just now I typed in wireless adapter into Google and it came up with 3,370,000 links. You just have to keep reading until it starts to sink in and make sense. You have to work at it. You will not be able to just ask somebody if you can hook your computer up to get wireless internet, and them be able to tell you. There are too many variables involved.
I hope you don't read this wrong and think I'm being harsh. I'm trying to help a fellow newbie learn!! If I can do it, anybody can. I went from not knowing what a network was, much less a wireless internet connection, to installing and configuring a satellite internet connection shared wired and wirelessly with 5 computers in 3 different buildings. All with the power of Google!!!