I can think of 2 possible ways to answer this question. Are you asking if your computer is capable of connecting to an ethernet network, or are you asking if your computer is already connected to an ethernet network?
To find out if your computer is capable of connecting to an ethernet network follow these steps:
1) right click "My Computer"
2) click "properties"
3) click the "Hardware" tab
4) click "device manager"
5) expand "Network devices"
The devices listed there are usually able to connected to an ethernet network. If you don't have any listed then you need to install an ethernet card in your computer.
To find out if your computer is already connected to an ethernet network follow these steps:
1) Click "Start"
2) Click "Run"
3) type "cmd" and press enter
4) type "ipconfig /all"
Look for a line that says IP Address. If that line has numbers, you should be connected to a network. However, if the numbers are all 0 or if the numbers start with 169, you might have an ethernet card, but no network connection.
Good luck.