You can connect your laptop to the internet with a cable modem, sure. You will need an Ethernet cable to do that. If you want wireless internet, you will need a cable modem, and a wireless router as well.
You can add internet connectivity buy purchasing a USB Modem, PCMCIA Modem
laptops and computers dont come with modems. They come with wireless adapters that are essentially the same for both laptop and desktop, that can connect to modems. If you have a purchased usb modem for your laptop, that is what is accessing the internet. If you do not, the modem, say at Starbucks, is accessing the internet for you...and you are connecting to it.
A wi- fi modem is a thing that gives you internet at home on the computer or laptop.
If you want to have internet on that laptop you need to be connected to internet provider which usually happens directly (connected to the modem) or indirectly (connected to the modem through wired or wireless router).
A router and the modem that will hook up to that router so it can provide the internet. Or you can wirelessly connect to the modem with Wi-Fi. You can also use a dongle for on-the-go internet.
install a wireless card on your laptop, and have wireless internet (via modem) in your home
You need to add a wireless access point to your wired internet.
wireless internet: for example you are able to use the internet on a laptop in your home without connecting it to a modem
No, but you are going to need a wireless router, also known as an access point, between the laptop and the cable modem.
Look at How can you speed up your wireless internet? for the answer
Is there a router that you can plug a laptop modem into so that I can get internet on my desktop also. The desktop would need ethernet and of course the laptop is usb. So is there a router out there that can do this?
Subscribe to an ISP for internet such as IVC Telecom and then connect your laptop to the modem with an ethernet cable or connect wirelessly using wifi, assuming your laptop has a wireless network card.