I'll be Your Flight Instructor
Before I go over techniques, I think it's worth mentioning that everyone has a different style, and it's best to see what works for you. But it's annoying to get blown to atoms 5 times in a row and not understand what's going wrong, so I'll go over some of the basic techniques that work for me.
You should also know a bit about who you're learning from. I consider myself to be an excellent dogfighter. Still, there are many players out there that are at least as good as I am, if not better. In general though, I can usually hold my own in a one-on-one match. Anyway, that where I think I stand, so you may or may not be able to learn anything from reading this section.
Sliding
Sliding is what makes Tachyon different from most of the popular space flight-simulators. Sliding allows you to glide in one direction while the nose of your ship faces another. This is a technique that I first encountered in Wing Commander, and while fairly important to use in that game, it is almost essential for dogfighting in Tachyon.
If you find yourself going head-to-head against someone, the basic idea is to point yourself either to the left or right of the opposing ship. Just inside firing range, kick in your afterburners to travel forward at an accelerated rate. The idea is to be moving fast enough so that you are hard to hit.
When you're in range to shoot each other, stop using your afterburner, and instead go into slide-mode. This is accomplished by using either the 'Q' key or button 4 on a joystick. It's important to note that afterburners and sliding don't work at the same time. While sliding, you can turn the nose of your ship so that you can fire while you pass each other.
If your opponent doesn't quickly turn around (this happens often if your opponent doesn't use sliding much), you can accelerate after you pass each other an end up on his or her tail. This is one of the best times to launch your missiles or rockets. Which brings me to my next topic...
Missiles and Rockets
Fighting with Galspan and Bora are fairly different. Since Galspan has lock-on capability, firing missiles at range can be effective. The main trick to getting your weapons to hit is to be on the opponent's tail. If you are both in a tight turn, it is a bad time to launch, even if you have a lock. Mostly likely your missiles would propel forward and the arc would be too large to accurately hit the target. Guns and lasers can be effective in tight turns, however, since there is little delay between firing, while missiles pause and drop before they engage.
With Bora, the key to using rockets is to be as close as possible. Hitting a target with lasers is hard enough, you don't want to waste your precious firepower. When using the slide technique, you will generally want to have another laser in your secondary weapon's selection. I link the primary and secondary with the '~' key, and keep them both on single fire to maximize firing rate.
Sliding and rockets can work successfully together, however, particularly if you have an opponent that slows down and spins around to face you. If the enemy slows down you can quickly destroy them with quick volley's of rockets. I like to duel-fire Spire Rockets because you get so many, but I single fire Plasma Rockets. It's difficult for any ship to finish off the opponent with lasers alone, so you don't want to waste ammo. With Plasma Rockets, even a single rocket hit will do massive damage, so duel-fire isn't much more useful.
As I mentioned in the equipment section, I think Bora Sappers are pretty worthless. They aren't very accurate, and while the idea of slowing or disabling the enemy is appealing, for every hit you make with a sapper you probably could have hit them with a rocket, which would have destroyed it. On the other hand, I once hit someone with a power sapper at the beginning of a duel, and they lost enough power that they couldn't fire back at me, making for a relatively easy kill. A rocket won't finish anyone with just one shot, so sappers do have some logic behind them.
Afterburners are Your Lifeblood
Forget about your hull condition. If you have a critical hull, but plenty of afterburner power, there's a chance you can escape. In general, I find that whoever runs out of Afterburner power first loses. When I run out of afterburner power, I usually find myself dead very quickly. On the other hand, I generally only fly the smaller but faster Pegasus and Mace, so rules may change with pilots of the Orion and Battleaxe.
Afterburners are essential for slide dogfighting. Without accelerating yourself before sliding, you will likely be too slow and will be hit by your opponent.
Punch your burners, slide, turn, fire, repeat.
It's also worth noting that while helpful in running away or quickly moving to and from portal/gates, afterburners should never be used for prolonged periods. Quick bursts are the most efficient, since your acceleration is much higher than your rate of deceleration. After you reach your max speed, continued use to maintain that speed will drain your afterburner power quickly.
You can change your rate of recharge with the 'B', 'N', and 'M' keys. Whenever something is charging, your engine power will be slightly lowered. Still, I find that setting all of these to the maximum recharge rate is the most efficient. After using my afterburners I may be a bit slower, but having more afterburner fuel quickly is a much greater asset to me.
If you need afterburner power in a hurry, you can drain your shields and get some extra burner power by pressing the 'G' key. You can then use the 'T' key to shift power from the lasers back into your shields. Unfortunately, there is no direct lasers to afterburners, but this works okay.
Naturally, shifting power from shields doesn't work very well if you're currently being bombarded by fire. However, I have found that sometimes I can shift power to afterburners, and then regains shields from my lasers, in order to escape an opponent. It's impossible to fight everyone, and in times when you need to move Credits quickly, or to escape, etc... thinking of your lasers and shields as afterburner reserves can be of great use. The biggest bonus from this is that your afterburners, shields, and lasers will all recharge, rather than just your afterburners.
Well, those are all the tips I'm willing to give up. = ) With practice, you should be able to win a decent amount of one-on-one battles. Even for a good pilot though, one-on-two is almost suicide. While you're on one opponent's tail, the other ship can be on yours. To effectively fight numbers, you need some backup of your own. Which leads us to our next topic...