So, despite your best efforts, you've jumped into a low sec system and found your overview decorated a jaunty red. Half a dozen pirates with propulsion jammers and a taste for blood. What you do next will decide if you're going home in your ship or your pod.
The first and most important thing is to... do nothing. When you first
arrive in a new system, your ship has what is called a "gate
cloak". Your ship should be transparent on your screen and, though you
can see the baddies, they can't see you. They will have seen the gate
activation, and they'll know who you are because your name will have
appeared in the local chat channel, but they won't know what kind of
ship you're flying or, more importantly, where you are. For thirty
seconds you will be invisible and invulnerable, unless you drop cloak
sooner by moving or activating a module. Take full advantage of that window of time. Appraise the situation as carefully as you can.
The first thing to do is look on your overview and see how far you are
from the gate. When you jump through, you could appear anywhere within
a 10km radius sphere around the gate. You can activate a gate from
anywhere with 2.5km. So, if you happen to be close, you should
seriously consider just jumping back through. But don't rush it!
There's a thirty second session change timer during which you can't
jump out of system after having entered it. Conveniently, this is the
same length of time that your gate cloak lasts for. So wait for your
gate cloak to drop on its own (or count in your head and start moving
just a little early) and afterburn back to the gate before they can kill
Another thing to look for is how far away the baddies are. The
furthest it is possible to warp scramble someone from is 29km and that
requires tremendous skill investment. For most pilots the practical
limitation is 20km or 24km. It's unlikely, but if all of the campers
are further from you than this, you should seriously consider just
warping off to the next gate. Even if they lock you, it's unlikely
they can put enough damage on you to kill you before you enter warp.
Finally, even if you're exactly 10km from the gate and they're all
right on top of you, all is not lost. for them to pin you down they
have to get a lock on you and activate their warp scrambler before you
enter warp. Smaller ships have higher agility and thus enter warp
faster and they also have smaller signature radii making them take
longer to get a lock on. The net result is that, if you're in a
frigate, you're generally going to be in warp in less than four
seconds from when you click "warp to" and the fastest locking ships in
the game won't be able to lock you in much less than 3 seconds. When
you add in reaction time, lag and the fact that not everyone is in the
perfect ship, frigates can almost always just push the pedal to the
floor and fly screaming, hair on fire, right through a gate camp.
Destroyers too, though at a somewhat higher risk. By the time you're
in a cruiser it's a much less feasible option.
You can improve your chances at blockade running in any ship size by
fitting the right modules. Particularly, either Nanofiber Internal
Structures (which increase agility and speed) or warp core stabilizers
(which allow you to ignore a certain amount of warp scrambling). Both are low slot modules. On the face of it, the warp core stabilizers might look like the more attractive option, but it's important to note that they
cripple your combat ability (dramatically reducing your maximum range and ability to lock onto other ships) and that each one only protects you against
one point of warp scramble strength. The baddies will likely have
multiple warp scramblers and some scramblers provide more than one
point of warp scramble strength. On small ships I'd say it is almost always
much better to go with the nanofibers.
If You Do Get Scrambled:
In all honesty, you're probably going to lose your ship. But that doesn't mean you shouldn't go down fighting. There will be a little blue
icon on the overview over the name of whoever is warp scrambling you.
Target that person and open up with your guns. Your goal isn't really to escape at this point, but the initial tackler is usually in the flimsiest ship and you might just manage to take someone down with you.
There is also the chance that they will try to ransom you. Basically,
if a pirate scrambles a ship that they know they can kill easily,
sometimes rather than doing so, they will start a conversation with
the pilot and offer to let it go free if a certain fee is payed. Feel
free to negotiate and certainly don't pay anything that is higher than
the cost of your modules and a new insurance policy (the base cost of
the hull will be covered by the insurance I hope you remembered to
buy). Of course you should also feel free to answer the ransom demand
with your guns. And though you in my experience most pirates honour
ransoms, you should definitely remember that there is no game mechanic
forcing them to do so. Taking a large payment in exchange for safe
passage and then promptly blowing up the person who payed you is
considered valid gameplay in eve.