Can my DIY Arduino be powered with 12V battery via lm2576 switching regulator?
If you are using something like the Arduino Uno that has a power jack, you can just directly connect the 12V to the power jack as the Arduino has an internal voltage regulator (although not a buck converter I believe).

Or you could use the buck converter IC (Lm2576) you mentioned and follow figure 1 exactly from the datasheet and place the output through USB or the 5V pin instead.