The first thing you need to understand is those pins on the ATmega2560 are not connected to anything on the Arduino Mega PCB. In order to use any of those pins you will need to get some hair thin magnet wire and super carefully solder that wire onto the tiny pins on the ATmega2560 microcontroller chip on the Arduino Mega board while making sure that the solder and uninsulated parts of the wires don't make contact with the other pins. This is possible but it requires a lot of soldering skill.
This video will give you some idea of what is involved:
In a way, they have it easier because they are working on perfboard while you're going to just have a bunch of thin wires hanging in the air, only connected to the MCU via fragile solder joints.
It's certainly doable but in the end you might be better off just starting from either a custom board or else a TQFP-100 breakout board. They sell universal TQFP breakouts like this:
Of course soldering a TQFP is a bit tricky also but I'd say a bit less than the magnet wire, especially with a little practice.
So you need to determine whether that's something you want to jump into and then make sure you have all the necessary equipment and supplies.
As far as the software side of things goes, there are excellent instructions on the MegaCore page I linked above. If you end up with any specific questions after looking at them then let me know.