SoftwareSerial with ATTiny84 using ATtiny library

If you can upload a working blink sketch to your Tiny, you should be able to use TinyDebugSerial, which is a one way communication.

void setup() {
  Serial.begin(9600);
}

void loop() {
  Serial.println("Testing..");
  delay(100);
}

The output from the tiny is pin PB3.

You the need a serial/usb converter to connect it to your computer/serial monitor

more on this:

http://www.ernstc.dk/arduino/tinycom.html

As you see you have other options:

  1. TinyDebugSerial
  2. SoftwareSerial
  3. Use TinyISP and Tinyknockbang
  4. Use TinyISP and Serial Relay
  5. Use TinyISP and Nullmodem