Android Mega ADK 2560 Arduino LED interfacing without shields

for the Arduino Mega ADK 2560, you need to buy either a USB host shield or a bluetooth shield so you can connect it to an Android phone using Android ADK.

If you want to use your Android phone as USB host and Arduino Mega ADK 2560 as USB slave, it is possible to do but you have to work a lot on the code. So I suggest you to buy a shield and use Android ADK library instead.

Yes, for moderately low current LEDs you should not need anything else, except a current limit resistor.

This is because the Arduino Mega ADK 2560 already includes the USB host interface chip, the part that would have to be added to a vanilla Arduino via a shield.

Bluetooth shields are another option, as an alternative to the ADK USB host interface which the board you have selected already provides, so you don't need a bluetooth shield unless you wish to have a wireless connection, or use a very old Android device which predates the ADK interface availability.

Actually connecting the LED would follow any of the arduino blink tutorials; typically though you would connect the LED and series resistor in series, with the LED anode towards the +5v supply and the LED cathode towards a "digital" pin. The resistor can go on either side of the LED. We connect the anode and switch the cathode with the I/O pin because I/O pins typically do better at sinking negative currents than at sourcing positive ones due to details of semiconductor physics.