Familiarise yourself with the in-game search function. You’ll need to use it extensively to trade & upgrade your stuff. Check for a list of useful search terms somewhere online. they’re sadly not in the manual (edit: you can search for anything, but “plan” for example will list the closest 30 planets. That’s what I meant by useful search terms).
Use all the drugs you can, all the time. Drugs can make you a better trader, a better fighter, a better leader, tougher to kill, earn you more money on missions and serve breakfast & blowjobs in bed. Drugs are goood, M’kay?
Restart the game, pick better skills & pick a rocket launcher (and I’d suggest an engine) as your starting gear. Early in the game rocket launchers kick ass, especially upgraded rocket launchers like the one you can start with.
Talk to the other ships. It’s pretty hard to piss everyone off in SR2 unless you’re really trying, so chances are there’s nifty trades to be made with trade vessels, backup to be had if you’re getting attacked, and willing cronies if you decide to rob someone.
Get a shield right away. Apart from you and the odd Dominator-hunting armada, nobody are dumb enough to attack people they can’t scan. It means that if there’s a negative difference between their scanner rating and your shield rating, they’ll leave you alone unless you attack first. If the difference is positive (from their point of view), they’ll take you if they think they can. And early on, they can.
Explore Black Holes. The gear you find in them is never crap and sometimes pure awesome. Auto-repair, energy weapon boosters, fuel-regenerators & massive improvements to your jump drive are typical examples.
Don’t use auto combat. The idea is nice & all, but in practice it’s shit. Aim your weapons and remember you can shoot down rockets & the like.
Get your gear & hull upgraded as soon as possible, even if it’s shit gear and a shit hull. Money are easier to come by with upgraded gear, and your expenses will be lower.
Pay attention to your faction standings. The more people like you, the more they’ll pay you & help you against enemies/pirates. The more some dislike you, the more others will like you.
Learn what services the different bases offer. It’s another of those seemingly insignificant things that’ll have a major impact on the course of your career.
Check the ranger highscore. Find one of the Top 10 Rangers with the in-game search. Add the info to your info-bar so you don’t forget it. Track him down & observe how he plays. One of the coolest things about SR2 is that all the NPCs in the game are playing the same game you are, so hanging out with a proficient NPC is a great way to get a clue. Imagine how cool TES games would be if they worked like that… I digress, sorry.
Ask specific questions, because SR2 is very much an endless bag of gameplay tips & tricks.
