Before shooting a fight sequence, learn about fight choreography!
This might seem self-evident, but, trust me, it's not. The number of people who believe they can choreograph a fight because they've been in a bar fight or seen a few UFC matches is huge. However, movie based fight choreography is very different from actual altercations. In real life, people tend to throw a few wild punches at people, get snarled up in the other person's arms, and then one of them falls on the other. This does not make for captivating viewing! In order to make it interesting to watch, there needs to be a dance of motion, where each actor knows his/her part explicitly. Start by watching well choreographed fight scenes like those in The Matrix, Hard Target, or The Transporter, to get a feel for the way in which the choreography is tied to camera angles, shot lengths, and editing. Then read a book that deals with the intricacies of fight choreagraphy. One that we've found very helpful is, Fight Choreography: The Art of Non-Verbal Dialogue. Finally, if there's a high quality karate or martial arts dojo near you, consider working with one of the senseis there to see if they would be willing to teach your actors some "bunkai." Bunkai are “applications” that come out of kata—or “forms”—that the instructors teach at their schools. (Bunkai is a Japanese word applying to karate, so art forms originating from different countries will have different names for these applications.) These applications are often sections of fight choreography that train an attacker and defender how to move in sync with one another. While most of these bunkai need to be stitched together to make a full fight, some of them are extremely long and could be used as an entire fight sequence. Some are even designed to be waged against two, three, or four attackers.
The use of gas-blowback Airsoft guns and post-production muzzle flashes sold a truly authentic gun fight in Alex Ferrari's Broken. (Picture courtesty of Numb Robot, 2005; Whatisbroken.com )
If you want gun fights, consider Airsoft Guns and post muzzle flashes!
Getting actual guns is dangerous and expensive. The blank ammo is costly and having a professional armorer on set for safety is even more so. As such, consider getting some Airsoft guns that have realistic blowback functions. Microbudget action film phenom, Alex Ferrari, used this trick for his short, Broken, to amazing effect. Once you film the guns firing, you can add muzzle flashes in AE through DIY tutorials or through professional plugins like FXHome's Muzzle Plug. Standalone particle generator particleIllusion can create muzzle flashes as well as expended ammo, and has been used in numerous Hollywood films and TV shows. (In fact, I spotted some of the explosion options in particleIllusion being used to augment practical explosions in the most recent Rambo movie.)
Practical smoke effects made an impossible stunt believable in The Guardian. (Picture courtesty of Nick Denney, 2009)
Need explosions, consider adding practical effects!
Although it can be very tempting to want to create all your explosions in post, this is actually a bad idea. While post-production explosions can augment what you did on set, it's rare that you can make them completely artificially and have them be believable in your film. (At least, not on an microfilmmaker's budget. If you had all of ILM involved, it might be a different story, although I've seen some pure digital work from ILM that has been very underwhelming.) Now, as with all things practical, if you are working with explosives, you need to have an armorer on set with you.
Some things that don't use traditional explosives are Works bombs, which involve putting a toilet bowl cleaner such as The Works (which is largely hydrochloric acid) into a plastic soda bottle along with torn up aluminum foil. When the bottle is sealed, a chemical reaction between the acid and the aluminum creates expanding smoke which will eventually swell the bottle until it blows up. If quickly buried in some light sand, these explosives can look amazingly like grenades or heavy weapons' fire blowing up part of your background. (Even though these aren't traditional explosives, they can be dangerous, so do not use these unless you are prepared to accept these risks.)
If you don't want something that can actually explode, adding smoke bombs, using dry ice, or using a smoke generator can be great ways to augment something on set. In a recent movie I was the cinematographer on called The Guardian, a main character had to stop a truck that would smash into his invulnerable body. Rather than showing the impact which would have taken up far more CGI skill and time than we had available, we planned a series of creative cuts and post-production particle effects to sell the shot. Then we used a crane reveal to show the devastation. To sell the immediate destruction to the vehicle (which was actually a wrecked junker) we had smoke bombs which went off as the crane rose above the scene. These practical effects heavily sold the reality of the devastation.