Good question.
Most of this depends on the ships you have available to you. By far, the best way but also the highest risk is trade runs. You can make a lot of aUEC running missions too, but trade seems to be the biggest returns and risk. Right now, you can also do mining if you have a prospector, but that's really only a good way until you get somewhere around 200,000 aUEC ... then if you can, do trade. The highest risk is that the game will crash and you'll lose what you mined... but you have no financial investment in the loss so... nothing risked but an hour of game.
For me... and it's really individual thing... I like to spend a bit of time trading around Port Olisar, but it gets kind of monotonous after a while. You can also find trade routes that include outposts, and the other planets and their moons. My biggest haul so far was in 3.6.2 has been a run I did for a little over 300,000 profit in a Freelancer Max, and I was carrying a mixture of cargo. The next time I tried that, the game crashed... so YMMV. Just be aware that can cost you a lot. I don't recommend using more than 50% of your available funds at any event... I try to keep it around 20% max right now.