For boosting combat effectiveness, I'd recommend (in no particular order and probably forgetting a bunch of stuff):
Use good loadouts. There are some threads with guides on how to build a ship well as its a pretty involved topic.
Pilot aggressively and give orders. Hard to give concrete advise because it depends on situation, but try and identify lone or vulnerable enemy ships/clusters of ships and concentrate on them. Try not to trickle your fleet into the enemy if at all possible. If you see one of your ships winning a duel (usually a frigate/destroyer on the side of the map) give it an eliminate order to speed it up. For a combat specced character: maintain local superiority. Your flagship generally wants to be going after the most powerful thing it can kill comfortably - leave tougher targets until you have support.
Have a plan on how you're going to secure kills. This is again going to get better next version because the 'speed boost on overload' skill is changing, but currently it can be pretty challenging to actually kill an officered ship and not just chase it away for it to regenerate its HP (vent). This could either be being in a fast striker with high DPS they can't get away from, or disabling their engines with EMP so they can't run, or surrounding the enemy cluster with a group, or using ECCM'd missiles to pop them, or a sudden bomber strike... you get the idea. But enemies getting away to vent is rough.
Stack bonuses: every endgame fleet should have 20 nav rating in its usual deploy, even if its not using coordinated maneuvers. The damage boost from L1L, CR boost from L3L, and flux boost from T4L stack and are significant. Either mitigate the ECM loss (use short ranged fast strikers, use ECCM + missiles) or really commit to ECM (will be better next version).
Make sure your ships work together and keep an eye on their deployment. Eg: If a heayy ship is built to kill capitals and cruisers its probably going to struggle to kill frigates effectively: support it with other ships that are specialized for that role, possibly with temporary escort orders or just making sure those ships are in the same area. If a ship is meant to be a mobile striker that finishes targets off, have other ships that give pressure and drive flux up. If you have a lot of gunships that get in each other's way, consider getting some carriers or missile ships or increasing your ship's ranges so they don't crowd as much.