I assume you have two wall plates like that, one for the wall speakers and one for the ceiling speakers? Those will most likely connect directly to the speakers, so you need to connect the TV to an integrated amplifier or audio video receiver (AVR). Then connect the AVR speaker connections to the wall plates with stranded copper wire (14 gauge is good for general purpose).
You can test the speakers with a battery; 1.5V will work or use a dead 9V. Connect one side of the battery to the red terminal and briefly tap the white terminal with the other lead. You should hear a pop or click from one of the speakers. Just don't use a new 9V battery as it may damage the speaker. The popping sound will tell you which connection goes to which speaker.
Those speaker plates look like they use spring loaded connectors. Strip about 3/8" of insulation from the end of the wire, twist the strands together tightly, push the button and insert the wire into the hole. When you release the button the connector should grip the wire. The plug pictured above will give a better connection.