On the surface, downshifting is one of the simpler tasks involved in riding a sportbike-pull in the clutch and stab the shifter. But that perceived simplicity often catches riders (us included) out and we see even expert-level racers get lazy in their downshifts from time to time. Because so many actions are required at close to the same time when braking and downshifting are combined, and one hand is trying to do two things at once, it's easy to become sloppy without realizing it. Smooth downshifting requires blipping the throttle between each gear, to match engine revs with road speed. If your bike has a slipper clutch you can get away with imperfect downshifts, but as always, the smoother you are, the better.
It's important to position all of your controls properly so that you don't have to be a contortionist to reach them. Adjust your shift lever so that you don't have to reach for it to upshift or downshift. Set the clutch free play according to your owner's manual, and make sure you have as little free play in the throttle as possible; be careful that you don't adjust the throttle too tight so that the engine revs up when you turn the bars though. Your brake lever should be at a height such that when you are sitting in a comfortable braking position, your arm, wrist and fingers are not at an angle to each other. Set the lever position so that you can comfortably use two fingers to brake without pinching your remaining fingers when pulling on the lever.
Practice holding the brake on with two fingers while you work the throttle. Consciously hold the grip with your remaining two fingers rather than letting them hang free, and this will help with working the throttle as well as holding on if you have to combine steering with everything else. While braking and downshifting try to unload the weight from your arms as much as possible by squeezing your knees into the tank or bracing them against the fairing-the tank is shaped like that for a reason. Keep your elbows slightly bent, and your foot in position above the shift lever. When approaching a corner, be as fluid as you can when you let off the throttle and apply the brakes.
After all that, now we can detail the downshifting itself-the setup before the actual act is that important. The order in which things should happen is: Preload the shifter slightly; pull in the clutch; shift; blip the throttle; release the clutch. When blipping the throttle, use enough rpm so that you don't add too much engine braking when you let the clutch out, but not so many revs that the engine tries to drive the bike forward. On the street, your downshifting can all happen at a relaxed pace and you won't need much of a blip, but on the track try to accomplish the whole sequence as quickly as possible, almost concurrently. You can use a lot of force to preload the shifter, and you'll need lots of revs. With experience you should be able to catch the downshifts quickly enough that everything seems as though it is happening at once. This will help when braking hard from high speeds for a slow corner, as you'll have to squeeze multiple downshifts into a short amount of time.