Many ways to do it, here is my way...
Remove seat, remove tank. There may or may not be a couple more vacuum lines attatched to the carbs, if so pull them off (these will be on the engine side of the carbs, not the airbox side.) . Remove chrome side covers. At the throttle grip there are your two throttle cables coming into the housing. There should be a jam nut on each one. Take a 10mm wrench or a small adjustable wrench and loosen the jam nuts (standard right hand thread). Back the jam nuts all the way back off until you run out of threads. Then take an 8mm wrench and turn the adjusters in towards the throttle grip. Once you have them all the way in, the cables will be at their most loose state. Remove the three screws and separate the halves of the switch. Take a small screwdriver or seal pick and remove one of the throttle cables out of the throttle sleeve. Once one is out, the other will come right out. Let that assembly hang (careful it doesnt swing down and bang into the fender). One each side of the airbox is a bolt the bolts it to the frame. 10mm socket. Remove the two bolts. Do not slide the airbox back yet. On the airbox boots there should be a spring that goes around the boot right where it meets the carb. It sits in a groove. Using a small screwdriver or the radiator tool. Roll it back out of the groove towards the airbox.
Drain the carb bowls. With the choke lever in the full off position, reach in from the right side front of the carbs and push the choke (enrichener) slide towards the left to give you slack to remove the choke cable and pull it out of the way. Back off the screws on the carb holders. Maybe spray some penetrating oil on the screw threads prior to lossening them. Loosen them up very loose. Once you have that done, you are ready to begin pulling them. I prefer to put the rear tire up against a wall or put the bike in gear or find a way to hold the bike from rolling backwards. You can straddle the bike and put your legs behind the foot pegs if you like. I prefer to kneel to the left side of the bike. What you want to do is push the carbs backwards towards the airbox until the front of the carb bodies clear the carb holders. This will take a pretty good amount of push and wiggle. The reason I leave my carbs in the airbox and not slide it back first is so the carb bodies don't start to come out of the boots and make the travel backwards harder. Once you clear the fronts of the carbs from the holders, rotate the front of the carbs downward and clear of the holders. Then it is just a matter of slowly wiggling and working the carbs out of the left side a ways until you can get to the throttle cables on the carbs. Remove them and then pull the carbs out of the bike...
All of the throttle cable and choke cable ends are made the same way, with a small barrel attached to the end of the cable. The barrel can be pushed out of it's place after the cable is rotated around to pass out of the slot...
When you put them in, just do the reverse. Slide them in from the left part way and attach your cables then move them towards the center as you also guide the cables . Keep the front of the carbs down under the carb holders and tilt the rear upwards towards the airbox. No need to worry about them seating in the airbox just yet. Once they are semi lined up with the airbox boots, you will have to push them backwards and this will kinda compress the boots. Push them far enough back so that the front of the carbs can be rotated upwards and clear the carb holders. This takes a lot of backwards push force and the carbs will just barely clear the carb holders. Once they are up and lined up with the carb holders you should be able to slide them forward and into the resting position in the holders. Then you need to take like a radiator tool or some method of running inside the lips of the airbox boots until they are outside of the carbs. Do one at a time (this is tedious and frustrating at times). Once they are where they will fit over the rear mouth of all four carbs you can slide the airbox forward and secure the two mounting bolts..be patient. It is a bit of a PITA but it can be done..