OK, let's take this step by step !
First of all, uninstall the driver(s). To do this, click 'Start / Control Panel' then double click on 'Programs and Features'. After a few seconds this will produce a list of the software on your computer. Scroll down and up the list to find the software associated with your USB adapter, then click on it's entry in the list, then click on 'Uninstall' towards the top of the of the page. This will start the uninstall process to remove it, then re-boot your computer.
Re-install the drivers for the adapter, but make sure that you install the XP drivers not the Win 7 or Win 8 ones. You may have to go to the manufacturer's web-site to get the drivers. If you cannot connect on your own computer, borrow a few minutes on another one - a friend's or a public one, library or internet cafe. Save then to a memory stick if you use a different computer. When you install the XP drivers, make sure you use the correct sequence, my one likes you to plug the wi-fi adapter in about halfway through the install sequence.
Once you have the correct drivers installed, and the adapter sitting in a USB socket, you need to connect to your router. By this time you may have a pop-up in the bottom right hand corner saying something like 'Wi-fi ( or Wireless, or WLAN ) not connected. Wireless connections are available.' Otherwise, you will have a little icon for your wi-fi at the right hand end of your task bar, which may have a yellow dot on it or be coloured red. This icon takes different forms. One is a little bar chart increasing left to right, another common one is a miniature computer screen. Click on this.
A menu should then pop-up with a list of all routers within range, which should include yours. If it doesn't, make sure your router is switched on and has three green lights showing. Then click on the entry for your router in this list, then click 'Connect'. If you have security enabled on your router - and you should have - you will then get a box asking you to enter the passphrase / password. Type this into the box and click OK. Give it a few seconds to connect, and you should be online.
These are generalised instructions. If they don't work, post back with the exact make and model of your adapter - it should be printed on it - and I will see if I can find the manufacturer's instruction set. Or you can put the make and model into Google and get the exact instructions that way.