Do a barrel roll!

Sorry, couldn't help myself. First thing to keep in mind is that each space sim will behave a bit differently and have specific things you need to pick up to be good at it. That said, there are certainly some tricks that are nearly universal to the genre. Since most space sims will involve quite a bit of dogfighting I'll focus most of my attention there. First off, try to avoid head-to-head passes- while it's tempting because it's easiest to hit an enemy that's flying straight at you it's also easy for them to hit you, and you don't want to engage in a battle of attrition. Take a few shots at long range, then veer off slightly, but keep your enemy in view and as soon as they go past you try to jump on them then ride their six the best you can giving it all you've got. For aiming you need to learn to lead your target, and the ease of doing this varies greatly from game to game- it's one of those specific things I mentioned that you have to relearn to an extent for each game.

When it comes to evading enemies, if an enemy jumps on your six it can actually be useful to decrease your speed a bit (although this usually goes against your instincts in that situation), as this will let you make tighter turns and make it more difficult for your opponent to follow you through your turn if they haven't dropped their speed as well. If the specific game includes afterburners (or something equivalent) then pulsing them to vary your speed can make you very difficult to hit. Combine this with the previous tactic by dropping your speed, making a sharp turn, then hitting the afterburners- this will shake almost any AI opponent. If you're trying to evade multiple opponents at once then it's better to keep your speed high, make lots of turns (as you'll be dealing with fire from multiple vectors), and again pulse your afterburners to vary your speed. Against multiple opponents you also want to thin their numbers as quickly as possible, so it can be worth it to take a bit of shield damage to quickly take out one or two at the beginning of the engagement.

In games that include guided missiles learn what the best attack vectors are to use them. Fire a missile when you're approaching head-on or directly from the side and you're less likely to score a hit; firing one when you're anywhere from their 4 to their 8 is much more likely to score a hit. Most AI's also tend to change behavior when they're trying to evade missiles, and this altered behavior can make them easier to hit with guns- forcing an enemy to evade a missile from one direction and guns from another direction makes it much easier to score a hit as opposed to trying to hit them with just guns or missiles.

There are also plenty of additional things such a shield/energy management, dealing with capital ships, giving orders to wingmen, and the dreaded escort missions, but these things tend to be pretty game-specific, so you just have to practice and figure out the best way to approach these issues in each game.