DOTLAN EveMaps

Be able to afford a loss

Never fly something (or with something in the cargo) you can't afford to lose. Yes, not even in highsec. Meaning that you should not fly a ship you cannot afford to replace and refit.

Consent to PvP

You consent to PvP when you click "undock".
You are not safe in 1.0 security space. CONCORD is there to punish, not to protect. Get used to the idea.
In most cases, the only way to be 100% safe from agression inside the game is to be docked in a station. Being cloaked in a secret safespot could work too.

Everyone can scam - and so can you

Never grant corporation rights to stuff you can't afford to lose either. No exceptions.
People offering free stuff? Probably traps. Be cautious.
Free stuff usually isn't. Not even minerals you mine yourself.
If it sounds too good to be true, it probably is. Paranoia pays off here. Double-check everything.
Scamming and unethical behavior some would consider griefing is not only allowed, it is encouraged and rewarded by the game mechanics.
Harrasment or real-life threats are not ok, and you can get a shiny ban for them. Learn the difference.

Experience matters, not ISK or Skills

Just because some character is just a few minutes old doesn't mean he's a newbie. Many people have alts. The reverse is also possible, people come back after very long breaks, and characters are sold. You could see year-old newbies around too.
Skills that take less than 1 day to train are short skills. Over one week is long.
You're in this game for the long haul. Don't expect to do something meaningful in the grand scheme of things in the first day of your first trial account ever.
All other things being equal (experience, skills), superior numbers more often win a fight rather than superior ship value. However, things are hardly ever equal.
Total skillpoints count doesn't matter much either, it's level of relevant skills to the current situation that does. Yes, that does mean a 2 mil SP combat-oriented newbie could badly beat up a 60 mil SP industry-oriented veteran.

Bigger is not always better

More expensive stuff is not always better stuff.
Slightly better stuff usually costs many times more as slightly worse stuff. Choose wisely.
Tech-2 is usually cheaper and better as best named, but harder to fit. Sometimes it's not better. Other times it's not cheaper. And occasionally, neither cheaper nor better.
There are no "solopwnmobiles" in EVE. Everything you can fly blows up if it's shot hard enough.
With enough skills and experience, ship size really doesn't matter all that much.

Use the in-game info

Showinfo and Variants->Compare are your best friends. Use it on all stuff you can.
Always check your ship insurance before you undock. If it's a T2 ship however... not that important.

Unfair circumstances?

There is no such thing as "a fair fight" or "an unfair fight". There's only "a fight". Circumstances are irrelevant.
Just because you can fly something doesn't mean you should.

You will lose stuff, don't worry!

If you PvP long enough, you will lose your ship. It's only a matter of where and when.
If you logoff in space without a PvP timer, you're only safe after 2 minutes... and then only until you log back in. If you logoff with a PvP timer, it's at least 15 minutes. Bottom line, once a fight started, don't logoff. You'll only die anyway.
Somebody, somewhere has better skills as you have, more experience as you have, is smarter than you, has more friends as you do and can stay online longer. Just pray he's not out to get you.
If you lose stuff, it's almost always your fault. Really, only yours.