Once you start adding lights and other devices, you'll realize that you can power anything you want just by connecting the positive lead directly to the battery, however this is not always a good idea. If you just wire a device directly, then it can run regardless of whether the engine is running or not. This is not always a good idea. There are a few devices that you might want to be able to activate when the bike is shut down.
These might include
Of course the down side to this is that, if the engine is not running, then you are draining your battery, so MOST devices should NOT be wired directly to the battery.
It is much better to wire them with what I call a "link to ignition", meaning that no power can be supplied to the device unless the bike is running. For absent minded people like me, it's really better to know that NOTHING can possibly be powered if you have the key out of the ignition.
As an example, another rider was hooking up this complicated "wigwag" module to his bike, and asked how we might rig it so that the lights can ONLY be lit when the ignition is ON, and so that all the lights will shut off whenever the ignition is OFF. Here's how...
See the diagram below.
For this example, just ignore the details about all the complicated stuff in the upper left hand corner - that's just a "wigwag" lighting module, and the details are not important at all. Suffice it to say that the Orange wire (pin 87) is our "power" wire, and our goal is just to make sure that this single ORANGE WIRE gets +12V when the ignition is ON, and 0 V when the ignition is OFF. You could attach a light bulb to that orange wire, a radar detector, or a hot tub. It doesn't matter for the purpose of our discussion.Just ignore everthing except the goal to get +12V to that orange wire at pin 87 when the ignition is on..
This is very simple in concept. You just need to find any wire that is ALREADY powered by the bike only when the ignition is on. On the Gixxer, the solid brown wire (meant to power your tail running lights) can be used. Also any ORANGE wire, O/G, or O/Y on the gixxer can be used because all of these are "hot" only when the ignition is on. Let's use the brown wire for simplicity. Call this our "signal wire" because it is the wire that carries the signal that "the ignition is on".
You DON'T want to use any red wire -- since on the Gixxer, all red wires are "hot" all the time, even with the ignition off.
You might want to just power the device with your signal wire. But that shortcut is sometimes dangerous.
Your signal wire was not meant to handle any extra current like this - and if you start runnig extra devices from it, it can overload, melt and start a fire (worst case), or just keep blowing your fuses (best case). So be a little more sophisticated than that 
.
Instead, use an SPST relay: Radio Shack part #275-226, "30-amp auto relay" which you should be able to find for about $5.99. Attach it as shown. The relay does what it says - it relays a current signal. When a + current is run through pin 85 and out 86 (to ground), the relay is "activated", which then allows whatever line is at pin 30 to connect to pin 87. The bottom line - when the brown wire says "the ignition is running", the relay allows the current from the battery to reach our lighting module in the diagram (attached to pin 87, and we have achieved our goal.
You can use this trick for any device that you want to link to the ignition, and hopfully in this way prevent any accidental DBS.
Now you need to know "where do I find that brown wire?"
Take off the rear plastic to expose the frame and the wiring harness on the left side of the bike. Here you are standing at the left side of the bike, gas tank visible on the left side of the photo. The red arrow points to the wiring harness that you want.
Just peel back the black "Loom" (that's what electricians call a black plastic protective covering over the wires), and you'll find all these little goodies inside! There's no orange wire here, and we definitely don't want to use a red wire, so we'll strip the insulation off the brown wire and use that, as in the diagram. Also strip the B/W wire (that's the ground wire), so that you can connect your relay pin 86 to ground.
Some guys will heat the insulation with a lighter to soften it, then peel it back. I just put my wire cutter on it, and gently pull the insulation away, being very careful not to cut the wire underneath.
Now just make your connections as in the diagram. This last picture shows my SPST relay in place. The blue wire comes directly from the battery +, goes to pin 30 on the relay, and then another blue wire goes from pin 87 to my fog lights (in the diagram, this is an orange wire going to power an electric module). NOTICE THE FUSE (WHITE IN THE UPPER RIGHT) -- YOU CANNOT FORGET TO PUT A FUSE IN LINE WITH THE "LOAD". If you're powering most lighting devices , 15 amp is a good fuse to choose. Fuse holders are dirt cheap -- at any radio shack, just wire a 15 amp fuse in as shown.
" Just out of curiosity...can't I just run the ORANGE wire from the module to the BROWN wire on the bike and skip the whole relay? Is there a particular reason why we run the ORANGE wire through the relay and not directly to the BROWN wire on the bike?"
That's good thinking, and it could be done that way from a "logic" standpoint. But from an "electrical" standpoint I don't think it's wise. I say this because you have the potential to draw dangerous amounts of current through that little brown wire.
Realize that the stock Suzuki wiring is VERY FEEBLE -- most wires are really only 20 gauge. That means it could safely take only about 8 amps of current a distance of 13 feet. The headlights if lit together will draw 9 amps of current. The Zuke guys did NOT expect wiring fetishists like you and me to come along and light up the bike like a Christmas tree!
That brown wire was only designed to take a SMALL amount of current to the rear of the bike to the tail running lights. It was never intended to carry current for the tail lights + whatever else you may have connected to it, (like front running lights if you're like me) + the full load of two headlamps. Not a good idea therefore to allow all these devices including the two headlamps to draw current through this one feeble little brown wire all at the same time. If you are lucky, you'll just blow 30 fuses. If unlucky, melt the wire and start a fire or permanently damage the electrical system of the bike.
The point of the relay is to switch a HUGE amount of current (like 9 amps for two headlights) ON and OFF by using only minimal current flow from that brown wire. Use nice big wire (like 14 gauge) to run from the battery to the relay, then from 87 to the module, so there is plenty of "room" in this thick wire for two headlights to draw current without producing damage or melting wires.
The brown wire will have almost no extra current draw through it as a result of the setup in my diagram because the relay coil (pins 85 and 86) takes only 0.16 amps in order to "activate" the coil and turn the relay "on". Again, what you're doing with the relay is allowing only a barely detectable current draw through a thin brown wire to use only 0.16 amps of current to turn ON and OFF a HUGE current draw of 9 amps to the headlights (the huge current goes from the battery to pin 30 to pin 87 to the two headlamps without ever touching the brown wire). COOL, eh?
So every one is happy.
Mr. skinny brown wire is happy because no extra current is really being pulled through him, so he's a nice normal temperature, and won't melt his outer coating away. Nothing more embarassing to a wire than to be caught naked!
Mr Fancy Lighting Module and his cousins the headlight twins are really happy, because now they can draw as much current as they need to be bright and healthy -- you've given them a nice power line of 14 gauge directly to the battery. The relay itself, by the way, is capable of allowing 30 amps (!!!) through the 30/87 connection before any damage to the relay occurs. That's much more than you'll need. The headlight twins only ask for 4.3 amps each on high beam.
Mr. GSXR Rider is REALLY happy -- because he has the coolest lights on the block!! AND now his cool Gixxer ass won't be lit on fire when he turns on the ignition!