How to use Arduino Bluetooth module?
It looks like one of the many BTMxx or HC-xx series BT modules, I have a couple here of the HC05 variety with the exact same layout but different AT commands. It can get confusing...

Luckily that datasheet is actually pretty good, many vendors don't even link to one even though they do exist (just try asking a few of the eBay seller out there and see how many positive replies you get ;-) )
Unfortunately typical is the fact they didn't also give you the detailed BTM-05 AT command guide, which you would need to change the all important baud rate (since it's not given in your datasheet)  

The AT commands (an old command type originally used with modems which stands for ATtention) are used to set various setting on the module (baud rate, name, role, etc) Usually you are only bothered about the baud rate and possibly role (master/slave)
They are detailed on page 4 of your manual. To use the AT commands you must set the command pin (pin 2) high to enter command mode, then send the command followed by \r\n. If the command pin is low you are in normal communication mode, where anything you send to the module will be transmitted.

Here is a snip from the AT command guide showing the baud rate command: 



The lack of detail or examples can still make things confusing for the new user. TO use the above to set the baud rate to 9600N1 (9600, no parity, 1 stop bit) you would drive the command pin high and send:

AT+UART=9600,0,0 

If successful you should receive OK back.

To query the current baud rate you would send:

AT+UART? 

If successful you would get back +UART,9600,0,0 (assuming it was set to the above)

To find it, I think all you should need is power applied - I could see my module when powered on. It's possible the device is in master mode and not visible.
A good way to test the module is active would be to send AT over the UART and see if you get OK back. If successful you know it's working (at least to some extent). Then check the settings using the other AT commands.