So when you want to fly the ship, you roll two dice and add your Piloting skill. When you want to launch a missile, roll two dice and add your Combat. The difficulty is the only thing you need to know... what do I need to roll?
Your referee should get a basic idea of how to play the game before putting you on a mission. Work together to figure out the difficulty of a given roll. The first few times you play, you'll probably miss a few factors, like, what's this thing called, 'OOC'? Is it contagious? (OOC is 'out of control,' it's a penalty to your checks when the ship has been upset by a maneuver or ram.)
Score the playing piece hero cards before cutting them. If there's a tiny incision along the cut lines, the board bends more easily and does less stress damage to the laminated paper when it's bent:

And if you went for metal:


These figures were exquisitely painted by John Newman, and can be seen at our booth at the convention!
Your board should look something like this while you're playing:

Although you probably won't be flying a prototypical fungaloid ship...
We cut one of our ship control sheets in half, since you probably won't need all 8:

This lets us keep the control sheets near their ships, so the referee and the players don't have to bump elbows. Ironically, these two control sheets are shown near each other.
We like to use a huge die for our phase indicator:

This ensures that no one will pick the die up by accident, at which point everyone looks at each other and forgets what phase it is. Also having a strong sense of time (when the die finally turns to the next number) keeps the action moving! We got this die from Koplow games at a convention.
You can place dice next to injured fellows, and even color coordinate them:

In the above example, the bug is at negative 4 hit points, and the xeloxian has taken 7 hit points of damage. You can reverse the colors if you like, since when I staged this picture I wasn't thinking about it.
Using 3rd party accoutrements like Dwarven Forge can make your missions in Battlestations really stand out:


You'll find new ways to build out adventures when you use hallways and go colony-side!
Using a handy tote will organize your Battlestations in one place:


This was about $50 at an art store, but you can get gear like this at camping stores for around $20.
We use different cargo bay equipment markers and note which ones are which on our ship sheet:

That way we know what's used, where we need to go to use things, what got blown up when we take internal hits, etc.
Extra playing manuals are handy.
Combat:
Make sure to 'stay frosty' and peek, poke,
go on overwatch, and pop your way around
enemies! If you overextend yourself and
get clambaked, you have no one to thank
but the kerbites back at the cloning facility.
Engineering:
Transfer all power to one system at the
end of the round. Since each system that
has power loses one at the end of the round,
loading all the remaining power in one
system means you only lose one power.
You can transfer it back at the start
of the next round.
Piloting:
Pay attention to your speed. Accelerate
wisely so that you can get the most out
of your ship and your power. If you're on
phase 5, and you're going from speed 0 to 3,
you might want to consider only going to
speed 1 or 2, since you won't be getting
the benefit of movement this round, anyway.
Time your maneuvers so that whenever possible,
you'll ooc the ship last in a phase.
Speed is almost always your ally. It makes
you a harder target from all the bad guys and
gets you where you want to go, pronto. Just
make sure you can still handle the ship!
Prepare and don't be shy about asking for
assistance, especially when your Size 8
ship is barrelling along at speed 9
towards a sun!
Science:
Research
Make your questions narrow the field by half
whenever possible. A classic example is
picking a number between one and 10 (the
number is 4. If you pick one at a time it
may take you 10 guesses to get the right
answer. If you ask questions that narrow
the field by half (is the number less than
5? (yes), Less than 3 (no), it must be 3 or
4) it only takes 3 or 4 guesses at most to
figure it out.
Take Notes
Keep track of what you've asked so you
don't ask it again. I like to track it
on the back of my Scientist's character
sheet.
Don't ask dumb questions.
Whether a missile is a boarding missile
or a warhead missile, you're still going
to want to blast it. At the end of the
round there is no such thing as a dumb
question. Since used markers will be
removed, you can ask freebie science
questions like whether there is a
threat aboard your ship. The difficulty
is zero because you're asking a 'range of
zero' question.
Get targeting locks
Don't forget to get targeting locks on
all ships in a system. Even if they
appear friendly, they might turn against
you or you may need to use the teleporter
to escape to them.
General
Keep extra gear beyond your carry limit
on the floor at your battlestation.
Everybody should have a medkit.
Toolkits are really optional. A good
engineer almost never needs a toolkit
except when repairing a slagged module.
Have a trick or two up your sleeve.
If you have some drugs or a skill chip
in something totally unexpected, you
just might be the marine that saves the
day with a hyperdrive program or the
engineer that pulls that amazing maneuver!