You might have heard the term "left hand-" or "right hand drive" thrown around on many BMX websites. This is simply a description of the side of the bike that has the chain, rear cog, and sprocket. Many bmx hubs come with the option of a right- or left-hand drive. Some are on side-specific while others are ambidextrous- the can be used for let- or right-hand drive.
The standard on bmx bikes and every other kind of bike has always been right-hand drive, so one might ask why anyone would want to put their sprocket on the left side of their bike. The reason is simple: grinding. If you ride ramps or street on your bmx bike, you very likely have pegs on it and use them to stall or grind on ledges, ramps, or rails. If your preferred grinding side is the right side (this is a personal preference just like writing with one hand or the other), your sprocket, chain, and driver are in jeopardy of being mangled. You can get a tank-ish chain, a guard on your sprocket, and a guard on your rear wheel, but a much easier and more reliable solution is to just move your drivetrain to the other side of your bike.
This is easier said than done.
Most hubs are made by default to be used with the chain on the right side of your bike, commonly called RHD for right-hand drive. A LHD hub is made as a mirror-image of a RHD hub. A regular hub has teeth inside the hub or freewheel such that, when the driver rotates clockwise, the hub engages, driving the wheel forward. An LHD hub must be made so that the driver engages when the driver spins anti-clockwise, so the pawls on the driver (or in the hub, if you have a hub with the q-lite system, which subverts the dominant pawl/ring paradigm) engages the hub when turning anti-clockwise.
To move your drivetrain from right to left, you need to start by getting a new hub, or a whole new wheel, that is LHD-compatible. Buying an individual hub might prove to be cost-prohibitive because you will likely need a whole new set of spokes and pay a mechanic to lace up the new hub to the old rim. There are a few hubs on the market that can be easily switched from RHD to LHD and back easily such as the G-Sport Ratchet, but most hubs only swing one way. There are also LHD freewheels for those of you still stuck in the Stone Age, but those also require a LHD, reverse-threaded freewheel hub. Those are very hard to find these days.
The part about this switch that has the most people hung up is getting one's sprocket on the left side of the bike. With traditional bmx cranks, there is a drive hole and bolt only on the right crank arm and nothing on the left. This would leave one to believe that the sprocket can only be used on the right side of the bike, but that would make one WRONG. I will get to that in a moment.
Thank heavens for LHD-compatible cranks! Most modern cranks are now being made with drive holes in both crank arms so that the sprocket can be run on either side without much hassle. Take your crank arms off, swap the sprocket to the opposite arm, re-install your cranks and Bob's yer uncle, you have a LHD drivetrain. If you don't have the luxury of this novel application of technology on your bike, don't fear the structural integrity of the piggy bank, there's hope for you yet!
Conventional wisdom would tell you that swapping your crank arms is a bad idea because your pedals will work themselves as you pedal. In case you were unaware, left-side pedals are "reverse"-threaded tighten anti-clockwise) and right-side pedals have normal (tighten clockwise) threads. I have been told that the Wright Brothers are credited with this invention, but I can't verify that. Anyway, it is possible that reversing that system will result in wobbily pedals that will work themselves loose (due to a mechanical process called precession, which I still do not fully understand) but this is unlikely if you take a few basic precautions like tightening your pedals really, really hard. A little thread-locking substance like Loc-Tite 242 will help too, but that might be overboard. Always grease your pedal threads and torque them down tight. If you check them occasionally and keep your pedals snug in your cranks, they will not cause any sort of catastrophic accident. Just a little mechanical vigilance is all that's needed to avert a pedal/ crank separation disaster.
If you go this route to swapping your drive-side, you will encounter one other obstacle: your left pedal will now be on the right and the right pedal on the left. You may never have noticed, but most flat pedals are designed with a parallelogram profile so that the top platform is always nudged a little farther forward than the one on the bottom.
Left and right are mirror images of each other, so swapping your pedals is going to make them feel awkward under your feet. Awkward is a word with appropriate spelling, because typing or writing that word is, for lack of a better word, awkward. I can't do anything with that latter linguistic problem but the former mechanical conundrum has an easy fix: disassemble your pedals, swap the pedal spindles with their respective pedal bodies, and reassemble. This might be more difficult that it sounds. Disemboweling a pedal of it's bearings and putting it back together so that it spins smoothly takes some finesse. Take care and don't loose all those darn tiny bearings!
Regarding grind-sides, many bmx riders run pegs on only one side of their bike because that is their preferred grind side. Doing this limits one to grinding only certain objects and doing it only one way. If you roll up to a perfect handrail and it's on one side of your bike and your pegs on on the other, you might find a creative way to grind that rail by hoping over it, doing a 180 and grinding it backwards, or grinding up the rail. If none of those options are in your bag of tricks, you are going to just have to move on. The other option is to run four pegs and learn to grind in an ambidextrous manner. There is something ethereal and yin-yang about "completing the circle" and learning to spin both directions, bar spins and tailwhips both ways, opposite wall rides, etc that is worth exploring. Ask Dan Price about that.
Nevertheless, you are most likely going to have a preferred grind side and your chain should be on whatever side is going to see the least amount of abuse from grinding.