You will also need to tie your programmer to VCC and GND, but you can do that anywhere in your circuit, they just have to be the same source. The 6 holes on the board in a 2x3 are an ISP header.
The six broken out pins are the only ones I can use to modify the chip, maybe the Rx and Tx lines too? I don’t know which pins on the avr programmer correspond to the ones on the motor driver. I know what they are labeled but I don’t know which ones go to which
You need to solder a 6 pin (2 rows of 3) header in the empty holes in the middle bottom of picture 2 on the product page. Then plug the 6-pin connector from the programmer onto the header. Pin one has the extra line on the silkscreen; it is next to the diodes, closest to the L298 chip.