Electronic – Should I connect 3V3 in UART

You can definitely transmit data using just TX & GND.

Firstly, you want to hook up the ATtiny85 TX line to the FTDI RX line (yellow on the TTL-232R). Make sure that the USB adapter can handle 5V - I'm fairly sure even the 3.3V TTL-232R is 5V tolerant.

According to the example page for SoftwareSerial, you need to set the direction of the TX & RX lines in your setup function:

// include the SoftwareSerial library so you can use its functions:
#include <SoftwareSerial.h>

#define rxPin 2
#define txPin 3
#define ledPin 13

// set up a new serial port
SoftwareSerial mySerial =  SoftwareSerial(rxPin, txPin);
byte pinState = 0;

void setup()  {
  // define pin modes for tx, rx, led pins:
  pinMode(rxPin, INPUT);
  pinMode(txPin, OUTPUT);
  pinMode(ledPin, OUTPUT);
  // set the data rate for the SoftwareSerial port
  mySerial.begin(9600);
}

The baudrate will be 4800 in your case. The SoftwareSerial library doesn't seem to support CTS & RTS, so just make sure you aren't using them on the host software.

Check out the reference page for more details, where they talk about some potential timing issues which may be exacerbated if you're running at 1MHz using the internal oscillator on the tiny.

The manual has the user using hyperterminal to send a text-file with the contents of + in it. I think the escape is just +, not +++. Also, you have to wait a few seconds (two is default) of no serial activity before the escape character will work.

I'm not sure if sending a text-file causes the terminal to behave differently then just typing +, or +++, but it might be worth trying. Maybe it needs basically no delay between the three +++, or it does something else (if the escape char is just +)

Also, have you checked that your signals are not inverted? Maybe the usb-serial is defaulting to normally high, and the module wants normally-low, or vice-versa.

Confirmed in comments below as three + characters, or +++. You have to send it as a text file. I suspect that feeding hyperterminal a text file causes the three bytes to be sent as close to each other as possible, while typing them manually causes a ~200ms+ inter-character delay (e.g. as fast as you can manually hit the + key).

Apparently the device has a much shorter "enter AT control mode" timeout them other similar devices, (like xBees, or such).