If you only need to add a few LEDs, either permanently or temporarily for testing, you can simply connect the LEDs (or other digital devices) directly to the output pins of the Mega2560 board, taking into account some limitations described below. A single Mega2560 pin can be configured as digital output to control one LED.
When controlling the "On/Off" type of output device directly with controller pins all you should worry about is its power consumption. According to AVR tech spec, the maximum ("damage") current for a single pin in output mode starts with 40 mA, that is quite enough to drive most LEDs used as indicators. Likewise, any other directly connected device (actuator, integrated circuit, relays, etc) should sink the current no more than 20-40 mA.
Powerful output devices that have high-voltage or high-current consumption cannot be controlled directly from microcontroller pins, you should always use some kind of buffer circuit for such devices.
This can be a PNP transistor, a MOSFET or a relay. If you use a relay, make sure that it has buffered input itself (as mentioned above) or it's a low current relay having a coil with higher resistance:
LED CONTROL OPTIONS
74HC595 Shift Registers DM13A LED Drivers MAX7219 LED Matrix MUX for LED Drivers LED Bar Graph Indicator Direct Connection LED Configuration