There is a lot you can write about fighting a fish but I will make a few pointers that I hope can help and I am sure others can contribute.
Here are my 2 cents.
1. When a fish takes the bait, try to stay calm, it is difficult but try to, it will help you to think more clearly and not do something stupid that will cause you to loose your fish or injure yourself or someone else in the process.
2. Striking v/s not striking – depends on what you prefer, today’s hooks are so sharp that at times there is no need to strike just raising the rod and holding it firm is sufficient to drive the hook home, however I still strike. I fish with lures, and some sea fish have real hard mouths so I find it hard not to strike.
3. Always maintain steady pressure on the fish and do not let your line slack, with barbed or barb-less hooks, In a long fight especially the puncture that the hook has made will widen with pressures and if the line slacks the hook can just come off.
4. Adjusting the drag, again different schools of thought here, some say never, use your palm or thumb, never adjust the drag, While I use my palm I also adjust the drag, have always been doing so and never had a problem. With Game reels especially, lever drags shifting the drag is almost a must. It is a good idea to use a scale to adjust your drag, I must confess though I only do that on my game reels.
5. Stopping a fish, if you have strong fish on and he runs there is really nothing you can do but wait, if possible move with the fish to avoid obstacles that could cut or snag your line. You could use pressure to guide your fish away from objects. Applying pressure directly against the fish is least effective if you are trying to turn or stop the fish, if you want to try and stop a fish or turn it, you need to apply if from the side either side will do depending on the circumstances. Applying pressure from the side will throw a fish off balance and is more effective then pressure from over and behind. Bear in mind which way the current or water flow is and try to use it to your advantage or you will be fighting the fish as well as the water.
6. Fish do not try and cut the line against rocks etc., what they do is try and rub the lure or hook against a structure, rock or bottom, your line can get cut in the process. Try to guide your fish away from any such objects.
7. As line goes out of your spool, the spool diameter reduces, so the drag pressure increases because of decreased leverage, simple physics. Ensure your drag is adjusted well, 1/3rd to 1/4th (of your lines BS) experienced anglers on lever drag reels apply max pressure from the start and compensate accordingly with the shrinking/expanding diameter, of the spool.
8. Your rod is a spring use it to its best advantage during a fight. Don’t wind the fish in, your reel is not a winch.
9. A fish always looks slightly smaller in water than it really is. (hope this does not fuel the "one that got away" tails)
so never underestimate the fish.
10. Some may not agree with this, but it is my personal preference, when I have got a fish in real close and feel I have sufficient control over it I tend to loosen the drag and play the fish with soft hands, as the angles are now reduces and at such close quarters pressure could be more, if a fish is not hooked to well then the chances of a fish tearing off the hook is high if they make a sudden run at such close quarters.
11. Landing a fish is as important as fighting it, make sure you stay calm, do not try and lift the fish out of the water, gaffing or netting should be done in one smooth stroke, if you choose to beach the fish use the waves and current to your advantage, and guide the fish in. Pump with the wave, hold against it.
12. Your knots are important, when you are fishing fine diameter lines make sure the knot you use spreads the pressure over the line so that it does not cut into itself. Cut off a few feet of line after a long fight and before you start fishing again.
13. Take care of your equipment, check your guides regularly, overhaul your reel, clean the drag washers, check your line, test it and change it if required. Check your terminal tackle like swivels etc which often get neglected. Wash your equipment immediately after fishing especially when you do so in Salt Water.