That's a tough question because it is so specific to the situation at hand. It depends on the characters, the fighting style, the animation style, and what weapons you're given to work with.
However, here's some quick fight tips:
1) If there is any rule for planning a fight scene, it's that the fight scene needs to eventually look like it wasn't planned!
Fights are chaotic and messy, and maybe it's just my personal preference, but the more choreographed a fight looks, the more bored I am watching it. As an animator, fight scenes are the one place where we have a terrific advantage over our real-life actor counterparts! Actors must work closely with their fight choreographer and rehearse their fight over and over in order to try to create something that doesn't look *too* staged, but also doesn't result in anyone actually getting hurt. Inevitably, the vast majority of these scenes DO feel like two people trying to hit their marks and not injure each other.
As an animator, you don't have to worry about any of that, and can actually create something that has the ferocity and "messiness" of a real battle! To me, this is one of the single most exciting and fun things about animation, so I'm always extra disappointed when I see a fight scene on a demo reel or in a show or film that feels needlessly choreographed.
Yeah, yeah - I know I'm beating a dead horse with the reference thing, but if you're planning a fight scene, it's one of the most important steps.
My advice would first be to watch and absorb as much footage as you can of actual people using the actual fighting style you will be employing. Actors are generally not the best to look at in these situations, and I'd especially avoid any "wire-fu" or footage of people doing wirework to pull off their moves (such as Crouching Tiger, etc) because it throws the physics off so badly and looks so weightless (though some of the sword-fighting, for example, in Crouching Tiger might be terrific reference!). Instead, my advice would be to watch some mixed martial arts such as UFC or some Thai Kickboxing or things of that sort. Look for moves you can use in your scene, but at first, just watch and absorb. Maybe go to a gym and watch some fighters and get an idea of how quickly they move, or how their feet move when they punch, etc.
Once you feel like you're getting the hang of the style you're looking to recreate or stylize, then you want to spend some time figuring out your actual scene or scenes. How much time do you have to work with? How many frames per shot? How many shots? How many characters? Who will win? How?
Once you have that stuff nailed down, THEN you can start looking for shot-specific reference that can inform the blocking of the scene and help you plan a blow-by-blow choreography.
Fights should be dynamic! Stage them and cut them to be exciting, but (if it's for a demo reel) also to show off your animation. If every shot is a close-up of a face getting punched or kicked, that's going to tell recruiters exactly zero about your animation abilities, so pull that camera back and lets see what you can do!
4) My last recommendation, if you're animating the entire sequence of shots, would be to block them all in first before polishing any one of them. Maybe get the whole thing feeling 60-70% done. At that point, you can lock down your camera angles, lock down your edit, and figure out if you are missing any shots, or if the whole fight is clear and making sense. Once you have all that stuff locked down, then you're ready to get in there and polish them up on a shot-by-shot basis!
Hope that helps! Thanks for writing in, Yatin!