Using the TPA2012/TS2012 audio amplifier is pretty easy - the power, control and input pins are on the left. On the right are the speaker outputs.
The power and control pins are on a 0.1" spaced header. The speaker outputs are for 3.5mm spaced terminal blocks (included)
On the right there are the 4 output speaker pins. These outputs are Bridge Tied Load which means you must connect the speakers directly - do not try to connect these outputs to another amplifier! Use any 4 to 8 ohm speakers. Lower resistance means you'll be able to get louder audio (2.8W max into 4 ohm, 1.7W max into 8 ohm). You'll want to make sure your speakers have a wattage rating higher than the max power, so make sure your 4 ohm speakers are 3W+ and your 8 ohm speakers are 2W+. Otherwise you risk blowing out the speakers or otherwise damaging them with too much power
Starting at the top of the left side, there are two power pins, VDD and GND that are used for powering the chip. These should be 2.7V to 5.5VDC. There's no polarity protection so make sure you get the wires in the right polarity! Higher voltages will give you more power so if you want that full 2.8W you need to give it 5VDC.
You can turn off the amplifier for each channel separately. To turn off the right channel, connect SDR to ground. To turn off the left channel, connect SDL to ground. By default these pins have pullups to VDD so both channels are on by default!
There are four pins for the audio input signal. For right channel, R+ and R- and for left channel, L+ and L-. These are differential inputs. If you are connecting this to a device with differential outputs. just connect the + and - pins as indicated on that device's outputs. If there is only one differential reference, connect L- and R- together and tie that to your differential reference. If you are using every-day single-ended audio signal, connect L- and R- to ground, and L+ and R+ to your signal.
There are 1uF input series capacitors on all four pins so it is OK if your signal does not have audio bypass caps. If your signal does have audio bypass caps, you do not need to remove them, just keep them in.
The amplifier has 4 voltage gain settings. You can set the gain either by switching the pins on the onboard DIP switch or connecting the G0 and G1 pins to ground. By default the two gain pins have pullups to VDD so turning a switch 'on' is the same as connecting the Gx pin to ground.
If you set the gain to 6dB that means you are 2x the voltage - so if your audio signal voltage is 0.25V peak-to-peak, the output will be 0.5V peak-to-peak
If you set the gain to 12dB that means you are 4x the voltage - so if your audio signal voltage is 0.25V peak-to-peak, the output will be 1V peak-to-peak
If you set the gain to 16dB that means you are 8x the voltage - so if your audio signal voltage is 0.25V peak-to-peak, the output will be 2V peak-to-peak
If you set the gain to 24dB that means you are 16x the voltage - so if your audio signal voltage is 0.25V peak-to-peak, the output will be 4V peak-to-peak
When you set the gain, you'll want to probably set the gain so you have the highest peak-to-peak voltage that is still lower than VDD, if your signal gets higher than VDD you'll get annoying clipping sounds. The gain you set depends, then, on what voltages you have to work with, as VDD and also the signal level. You may want to start with 6dB and increase the gain until you get the signal levels you like.
There's no 'precision' gain setting, but usually whatever you're piping audio out of has more precise audio control, such as a digital music player.