Programming Code

So let's work with what you have.
First, external connections"
You need 220, 270 ohm resistors between pins 3 & 4 and your LEDs. You say you blew some LEDs, hopefully you did not blow the IO pins, or the '328 itself, by connecting them directly. Make the wiring this: pin to resistor lead, other resistor lead to LED Anode, LED Cathode to Gnd.
Move the switch on pin 1 to pin 5. You need pins 0,1 free for the device to talk to the computer. Wire the switch so that when it is pressed, the pin is connected to Gnd.
Do the same with the reed switch - when the reed switch closes, it connects the pin to Gnd.

Now the code. You're close, just needs some tweaking. Compare this to yours, you can see what's changed.

// this is a comment, add as a line, or add at the end of a line
int manual_switch = 5;   //moved from pin 1, changed name
int reedSwitch = 2;
int ledRed = 3;
int ledBlue = 4;

byte  switchState ; // variable to store the state of the switch if needed
byte  reedState ; // variable to store the state of the switch if needed

void setup() {
  pinMode(manual_switch, INPUT);
digitalWrite(manual_switch, HIGH); // enables internal pullup resistor. Pin will read as HIGH when switch is open
  pinMode(reedSwitch, INPUT);
digitalWrite (reedSwitch, HIGH); // pullup resistor enabled
  pinMode(ledRed, OUTPUT);      // sets the digital pin as output
  pinMode(ledBlue, OUTPUT);      // sets the digital pin as output

Serial.begin(9600); // enable serial interface for sending messages out
}

void loop() {
// if switch is not pressed, the red LED stays off
  if (digitalRead(manual_switch) == HIGH) {
  digitalWrite(ledRed, LOW);
  }
// but when its pressed, make the LED flash
// don't need to read it again, has already been read
  else  {
    digitalWrite(ledRed, HIGH);   // sets the LED on
Serial.println ("Red on!");  // add a debugging statement - if the LED is not on, check the wiring.  Perhaps change pins if you suspect the pin is blown
    delay(1000);                  // waits for a second
    digitalWrite(ledRed, LOW);    // sets the LED off
Serial.println ("Red off!");
    delay(1000);                  // waits for a second
  }
// do similar for blue LED?
// if switch is not closed, the blue LED stays off
  if (digitalRead(reedSwitch) == HIGH) {
  digitalWrite(ledBlue, LOW);
  }
// but when its pressed, make the LED flash
// don't need to read it again, has already been read
  else  {
    digitalWrite(ledBlue, HIGH);   // sets the LED on
Serial.println ("Blue on!");
    delay(1000);                  // waits for a second
    digitalWrite(ledBlue, LOW);    // sets the LED off
Serial.println ("Blue off!");
    delay(1000);                  // waits for a second
  }
} // end loop