If you are using on-board sound (ie off the motherboard) then the speaker output is the green socket, and your speakers should be connected to that. If you are using a separate sound card, then refer to the manufacturer's documentation, that will tell you which hole does what.
Since you have given us no information on the make and model of either your computer or your speakers I am going to have to be a bit vague here. Go into your control panel and its sound or audio settings and check that your audio is enabled or set active or default.
Finally, check that you do have drivers installed for your sound system - find your way to 'Device manager' and see if there is a yellow exclamation mark against your audio. If there is, probably you do not have drivers installed. This screen will also give you the maker of your audio system, you can always check their web-site for drivers.