Confused on how to setup up a 2 by 2 button matrix?

http://playground.arduino.cc/code/Keypad

You won't need external resistors or diodes because the library uses the internal pullup resistors and additonally ensures that all unused column pins are high-impedance.

#include <Keypad.h>

const byte ROWS = 2; //four rows
const byte COLS = 2; //three columns
char keys[ROWS][COLS] = {
  {'B','1'},
  {'I','2'},
};
byte rowPins[ROWS] = {5, 4,}; //connect to the row pinouts of the keypad
byte colPins[COLS] = {8, 7,}; //connect to the column pinouts of the keypad

Keypad keypad = Keypad( makeKeymap(keys), rowPins, colPins, ROWS, COLS );

void setup(){
  Serial.begin(9600);
}

void loop(){
  char key = keypad.getKey();

  if (key != NO_KEY){
    Serial.println(key);
  }
}

For 5x2:

const byte ROWS = 5; //four rows
const byte COLS = 2; //three columns
char keys[ROWS][COLS] = {
  {'B','1'},
  {'I','2'},
  {'N','3'},
  {'G','4'},
  {'O','5'},
};

And add pins accordingly.