Assuming this other computer is not located near your router (in which case you would just run a cable) the first thing you need is to make sure this computer has a working wireless card that is compatible with your router.
There are four flavors of wireless - A, B, G, and N. A is rarely used these days and not compatible with the rest. N cards and routers are usually backward compatible with B and G, but check. G is the most widely available.
Once you have a computer with a compatible card that you know is working, just connect it like you did your first computer that's on the network. In some cases, you may have to power down all of your devices and then re-boot "from the wall out" - first the modem, then the router, finally the computer(s). It's that simple. Most wireless router are configured by default to accept a number of simultaneous connections.
If for some reason the above fails, check your computer and make sure the wireless card is activated (Device Manager) and receiving - you should see some kind of indicator on your computer or the card depending on your equipment.
Still no connection? Check the settings on your router. Did you enable security (WEP, WPA, etc) or turn off broadcasting? You'll need to make those settings on you new computer. Specifics of this can be involved and depend on which method you use.
One can connect an usb adapter to an access point by simply plugging in the adapter to the PC and using the software which came in a CD along with the adapter.In case there is no software for your adapter,then you can make use of the built-in utility for wireless connection in your operating system.
An ethernet cord to connect the XBox to a router or the wireless adapter for XBox to connect to your wireless router.
For such purposes you need at least two subnetworks. One adapter cannot be in the same time in both of them. Thus you cannot do that. If you connect your PC through wireless to another PC, and that PC is connect to the router with a LAN cable that it's doable.
A wireless USB adapter allows a computer or wireless device to connect to a wireless router. It is needed for any device which is not wired to an internet connection, to connect.
Your router WILL need to be wireless to connect wirelessly to your Xbox, but you can use an ethernet cable if your router is not wireless, straight from the router to the XBOX
If you have a wireless router just get a wireless adapter for the computer. It can be USB or PCI adapter. And connect your new adapter to the router in the same way as you connected the first computer.
You need an Xbox wireless adapter.
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If you want to use internet wirelessly, yes you need a wireless router and a wireless adapter for your PC (usually laptops have it).
You need a Wireless adapter, or a ethernet cable connecting to your home router.
Yes, you can. You have to configure your router to work in compatibility for G networks.
You need to have a wireless router compatible with your wireless adapter and LAN cable of CAT-5 at least. Use the cable to connect the modem and the router, use WAN port of the router. After that configure the router for your needs. And you are ready to go.
There are tons of reasons. Most common are secured wireless is enabled, MAC table is enabled, your wireless adapter is not compatible with your wireless router, wireless router does not work properly and so on.