TDA2030 (and the others in the series, like the much better TDA2050 for example) can be run with split power supply or with a single power supply - the circuit is slightly different but not by much.
See the attached datasheet, at page 8, you will see example circuits for either split power supply (where you would use at least +6v and -6v supplies to power the board), and an example circuit which can run with a simpler supply of just +12v or more.
The chip requires a minimum of 12v to work (or -6v supply AND 6v supply for a total of 12v difference) and can work with up to 36v ( or -18v AND +18v in split power supply mode) - see page 3 in the datasheet where these numbers are shown.
The efficiency of this kind of amplifier (class AB and average performance wise) is at around 60% , so it needs a lot of voltage to output a reasonable amount of sound, and it also heats (hence the heatsinks on it).
You can look on page 5 of the datasheet and you'll see there figure 4 and figure 5 .. output power vs supply voltage ... you should only care about figure 4, where the drawing is for distortion of 0.5% ... the other figure is for distortion up to 10% which is not great for music (but if you want to make an amplifier for announcements in a train station for example you wouldn't care about music and this would be acceptable)
So back to figure 4, you can see there that 4 ohm speakers are easier for the amplifier and it will output more sound power with 4 ohm speakers. So you can see there they don't even calculate how the chip would work with 12v ( or -6v and 6v) , they start right from +/- 8v (or 16v dc) ... at that point you can see that the chip can output just a bit over 2w on a 8 ohm speaker, and just around 4 watts with a 4 ohm speaker.
So basically, you need a much higher power supply to use this amplifier, my suggestion would be using one of those laptop adapters that output anything between 16.5v and 19v, they should be super easy to find.
Alternatively, you should look for a 15v..24v AC transformer and use a bridge rectifier and a capacitor to convert this 15v..24v AC to around 20..32v DC. As long as the voltage will be below the maximum this chip supports (and below the input capacitor's voltage rating on the board you have .
So also look at the voltage rating on the capacitors on your board and if for example it says 25v on the capacitor, then you shouldn't use more than around 24v at the input, unless you replace the capacitor with one rated for higher voltage (35v or 50v rating)
For testing that the board actually works, the easiest for you would probably be to connect two 9v batteries in series. Though note that 9v batteries aren't really designed to give a lot of energy to devices, so the amplifier chip may try to take too much out of the batteries and then the voltage on the batteries will drop quickly.
I'm attaching the tda2030 datasheet below: