PINS: The pins found on the breakout board are,
KEY: This pin has to be pulled high to enter AT mode.
VCC: Indicated range is 3.6 to 6 volt. To be on safer side, you should connect it to 3.3 Volt.
RXD: Serial input pin.
TXD Serial output pin.
STATE: May or may not be connected to any pin. Supposedly outputs the Bluetooth connection status. This pin will not be needed.
Some of the breakout boards have EN pin or even WAKE UP pin instead of KEY pin. None of them seem to be connected to any pins of module. But that does not matter because we wouldn't need them anyway.
Once you identified the module, now it's time to enter the AT mode.
For HC05: Connect the Rx pin of the Bluetooth module to Tx pin of USB to TTL converter, and Tx pin of Bluetooth to Rx pin of converter. Also connect their ground but don't connect the Vcc yet. First you'll have to short the key pin with the Vcc. Connect key pin and Vcc together on breadboard, or any other way. After all other pins are connected, connect Vcc of bt module to USB to TTL converter's Vcc. Now the led on the module will blink at the interval of 2 seconds. That means it has entered the AT mode. If the led blinks faster then AT mode was not entered. Disconnect Vcc, check your circuit and try again. If it does not work then there's a chance that your KEY pin of the module is not really soldered to the KEY of the main chip, i.e. the 34th pin. You can check that with the help of multimeter.
If you use an arduino uno, then connect Rx pin of the Bluetooth module to pin 11 of Arduino Uno(supposedly same for arduino mega), and Tx pin of Bluetooth to pin 10 of Arduino. Also connect key pin of module to pin 9 of arduino and ground to ground, but don't connect the Vcc yet. You have to first power up the arduino, and then connect Vcc just like you did in case of USB to TTL converter.
For HC06: Just connect the Rx of module to Tx of usb-ttl converter and Tx of module. Connect ground and Vcc. The module is in AT mode. Didn't see that one coming, right? :P Turns out HC06 module is permanently configured to be slave and it is always in AT mode when not paired to any other device. So there is no confirmation led blinking that it is in AT mode like HC05 has. Just power up the module and pass the AT commands to modify the default settings.
HC05 USB to TTL Arduino
Vcc Vcc Vcc
Rx Tx pin 11
Tx Rx pin 10
Gnd Gnd Gnd
key Vcc pin 9
HC06 USB to TTL