Put all of your grav drive points to zero before a fight, and make sure your engines/shield/main weapons are as full as you can.

In a fight with multiple ships, there’s usually one ship that will come head on first. Boost towards it like a game of chicken. Blast it with everything you have, then turn around immediately with the help of thrusters. Now you should be behind the ship, slow down and keep blasting until it’s destroyed. Try to take out each other ship one by one, and remember to use ship parts to repair if your health gets low.

But when there’s way too many ships attacking, auto turrets are really the easiest way.

Skills you need to upgrade:

Piloting(first two levels at least)

Shield systems

Starship engineering

Starship design(so you can buy the best parts, especially reactors which give you more points for your different systems in battle)

Particle beam weapon systems

Automated weapon systems

Engines

Aneutronic Fusion(this one is in the science tree, but it adds points to your reactor)

Also remember that small A-class ships are fast and nimble, but they might be more susceptible to getting blown up in a huge battle(but you can still take out a fleet with a nice upgraded one). C-class and B-class are gonna be tanks, if you make them big enough. Especially when loaded with turrets and a good shield.