One of the coolest things about the micro:bit is that Bluetooth is built into the device. You don't need any extra add-on boards or connections, it's just there ready to go.
To put your micro:bit into pairing mode, you just hold down all three buttons at once. That is A and B on the front and the Reset button on the back. Hold them down for three seconds and the word "Pairing" will scroll across the screen.
Now on your phone go into the settings menu. On an Android just swipe down from the top and click on the Bluetooth device button.
Now here comes the trick.
If your in a classroom with lots of other micro:bit devices you need to know which one is yours. Luckily each micro:bit has a name that you can read off the screen.
If you haven't done so all ready go to the Andriod store and download micro:bit blue. Get it here.
The devices name is set in the firmware. So you can't change it. Also, it is not visible on the screen printing on the circuit board as each micro:bit has the same screen printing. So I suggest putting your devices name on it. Perhaps like this.
Now you micro:bit is connected to your device and you have the app installed you can read the values of the sensors, set the state of the LED's and use the Dpad as a remote control!