Just like everybody else, I started doing the tutorials and then switched to the epic arc.
There is one mission where you MUST die, else I finished the whole arc without blowing up.
I learned a lot about weapon ranges, speed tanking, and armor types during the last few missions of the epic arc.
The final opponent is quite hard to kill, if you have very limited skill points (which I had after only 3 days playing). I spent the playtime of 2 days, just to find a way to finish that last opponent.
Finally I managed to kill him by getting in close, speed tanking and applying explosive damage. As a Gallente this was not an easy task, I fitted a Gallente destroyer with 200mm Autocannons to accomplish it (don't laugh, it worked. With blasters and thermal it did not).
I was very proud and promptly headed to lowsec with my ~invincible destroyer~ for my first PvP experience. Really. My toon was almost a week old and had a lot of skillpoints. I thought.
But the best part is still to come: I was immediately aggressed by a frigate and managed to blow it up! No kidding. Sadly I don't have a killmail and still don't know why.
I assumed it was because I was on a trial account and so I upgraded to a full account at once. And finally got killed by two Tristans.