This is my favorite tip:
Don't die.
There are many many ways NOT to die in Eve!
Say you are in a fleet at a gate somewhere, and a fight is about to go down. Your FC starts to call out primaries, and you notice that you are getting targeted, and start taking damage. Do you:
a) Follow FC orders and start engaging enemies, or
b) Quietly disobey your FC, tank the enemy damage for a while, and at the last moment, jump the gate?
If you chose B, you are creatively NOT DIEING in Eve. You have wasted the enemies time and attention. You have denied the fleet a kill! You can now burn back to the gate on the other side, jump back through, and re-join the fight! Even better if your logi can try to hold you up for as long as possible.
Now, as another example: Say you are in a tackle ship, interceptor or T1 Frig, or even a heavy tackle cruiser. You are first to arrive tackling a larger ship that has engaged you. You land a point, maybe do a scram pass, but his drones are all over you. Someone calls secondary tackle. Do you:
a) Immediately warp off,
b) Align to a bookmark or celestial, overheat MWD, and kite his drones out to 100km,
c) A or B, depending on the damage you are taking
The answer is, of course, C. Optimal not-dying is very situation-dependent. There are many, many factors, including your ships tank, the type of damage incoming (you may need to manually "Spiral Out" to maximize transversal).
Do NOT fall victim to the "Hero Complex"! Sometimes the hero tackle dies, and there's nothing to be done about it, and one might even say the trade-off is worth it, especially for a nice juicy blingy kill for the fleet. But you are FAR more valuable to your fleet ALIVE. A dead scout / tackle can be a big problem for a fleet, removing a critical source of intelligence for the FC.
A pilot should NEVER feel like they are obligated to stay in a fight if under pressure. Live and fight another day, even if that blingy ship gets away. Reshipping can really be a sucky prospect, and a fleet without tackle can have a hard time hunting and holding prey.
Thanks for your time, and fly dangerous (and fly safe)!