If you have a weapon that cannot damage an enemy ship's hull, keep firing at it to raise your crew's experience. You should disable your opponent's engines first to maximize the time you can fire at them.
Activate your cloaking device when your enemy shoots, whether they can damage you or not. This allows you to gain skill by dodging.
Time and cycle your shields wisely during combat to increase experience for the crew member operating the shields.
When attacked by an enemy that cannot penetrate your shield, avoid destroying them. Remain idle to earn experience for your engine, pilot and shield crew.
When you enter combat in an asteroid field, don't jump out after destroying the enemy ship. Get rid of your pilot to drop your evasion to 0% and allow the asteroids to hit your shield. This will increase the crew member operating the shields to gain experience.
Note: An unpatched version of the game is required. Power off the shield's subsystem then power it back up during an enemy battle. You will earn shield experience each time the shield powers on.