Go to Control Panel and select Network Connections.
If you have Wireless there will be an entry here for the wireless connection though it may say Disabled.
Rare for a desktop to have wireless, but look for an aerial about 4 inches long coming from the back of the processor box. Or you may have a USB adaptor but I am sure you would know as this is something you would have physically had to do.
Laptop more likely to come with wireless as standard, if it is a more recent model. What make/model is it?
Are you cable of phone line broadband? Need to ensure you get the right type of router. You say you are currently connected by cable , is this by a USB cable to a modem or using network cable (ethernet) to an existing router?