Oh ok, that appears to be a phone jack with an auxillary rj11 (standard phone) jack labeled 'dsl'. A regular phone wire plugs from that to your dsl modem. The dsl modem then has an rj45 (ethernet) port and you connect a cat5 ethernet cable from the dsl modem to your pc's port.
Here's a pic of the back of a standard/basic dsl modem.
http://www.hypersurf.com/images/dsl_modem_back_large.gif
The port on the left with the white square around it plugs to the small phone jack box in your hand in the pic you linked. The port on the right with the yellow square around it matches the network plug on your pc. Use a cat5/ethernet cable to connect those two together. You can't connect directly from the pc to the wall, you need a modem. It may be different depending on your location but usually the isp (internet provider like comcast or at&t etc) provides you with a modem. If not then you have to purchase one and contact your isp to find out if there are any specific settings needed to connect to their network.