So talking with a friend I decided to make a synth, a basic but nice one. So I thought why not? So I'll add my contribution to the APC history!
The Atari Punk Console has a long history so you can check it here.
I can tell you it was designed by the most famous Forrest M. Mims III.
It is called the Atari Punk Console because of the stepped tone generated is like the sounds emitted by the original Atari video game system.

Step 1: Materials

The electronic components you will need are:

X2 555 Chip (You can also use a 556 Chip but for sake of simplicity I will use two 555)
X1 1K resistor
X1 .01 uF ceramic capacitor
X1 .1 uF ceramic capacitor
X1 10 uF electrolytic capacitor
X1 Female stereo jack 6,3 mm
X1 DC female jack
X2 50K (or 500K but I will use 50K because it seems to me the correct stepped tone sound)
X1 Switch (any really)
X2 Knobs (optional)
X1 Prototype board for soldering (I bought the smallest and cheapest)
X1 Enclosure (optional, I used a plastic ipod touch one)
X2 8 pin sockets (optional)

Other things you'll find around the house:

Soldering iron
Screwdriver
Tweezers
Wire
Wire stripper

Step 2: The Schematic

So it's actually very easy.

First 555
Pin 1 goes to ground.
Pin 2 goes to .01 cap that goes to ground.
Pin 3 goes to pin 2 on the other 555.
Pin 4 goes to 9 Volts.
Pin 8 goes to 9 Volts.
Pin 7 goes to the pot and the resistor.
Pin 6 goes to the resistor and to pin 2 on the same 555.

Second 555
Pin 1 goes to ground.
Pin 2 goes to pin 3 on the other 555.
Pin 3 goes to output.
Pin 4 goes to 9 Volts.
Pin 6 goes to .1 cap that goes to ground.
Pin 7 goes to the pot.
Pin 8 goes to 9 Volts.

Pretty easy, huh!

Step 3: Making the APC Circuit

So you just have to wire everything up. I did this in 20 minutes and it finished pretty well.
I attached some pictures! Using sockets protects your IC from getting burnt.

OPTIONAL
You can add a switch by connecting for 9 Volts to ground.
You can add a DC jack, check polarity using a voltmeter.