Two 74HC595s (wired in parallel) will be driving all the LEDs in the project as well as providing power to all of the buttons. The 74HC595 is an 8 bit serial in parallel out shift register. I've written a detailed tutorial about multiplexing with the 74HC595, and you can find more info about this chip on its datasheet.

Each 74HC595 can only source 70mA at a time for all its pins. With the 100ohm current limiting resistors, if all 4 LEDs in a row are on at the same time (with multiplexing this is the max number of LEDs that can possibly be on at the same time), they will each draw about 18mA which puts the current requirements slightly above the 70mA maximum rating. I'll be drawing additional current from pins Q0-Q7 to multiplex the buttons (in later steps). An easy solution to this problem is to add another 74HC595 to the circuit, it will be wired parallel to the current 74HC595 (see schematic). This will give me additional 70mA to draw from on all 8 pins.

The 74HC595 can only do parallel output, so I used a 74HC165 to measure the state of the buttons via 4 current limiting resistors and send this information to the Arduino. More info about the chip can be found on its datasheet.

More info about wiring and schematics can be found in the instructions section.