Accelerating slightly about 2/3 of the way through a curve will enhance your traction. A downshift before the turn causes the car's weight to shift toward the front and helps "plant" the steering tires to hold the turn better. I like to give the steering a small sharp twitch in the direction of the curve just before entering a hard curve, with street cars and their relatively mushy suspension, this causes the car's body to "roll" as if you were actually going to hook the turn much sharper than it is, then rebound back in the opposite direction just as you actually enter the curve. In effect you are "cheating" the curve, giving the chassis a little unnatural momentum toward the INSIDE of the curve that it wouldn't have otherwise. Then you follow this momentum in as straight a line through the apex as possible, ending with the above mentioned light acceleration as you exit.
As said above, bringing the engine RPMs up to match the gear you are downshifting to makes for a much smoother shift, less wear on driveline and more control if shifting through a turn, but it takes a lot of time and practice to master.
Once you get the feel of what your engine sounds like at the points where you shift in different situations, you can actually float the gear changes without the clutch. Upshifts are easier than downshifts to float. On an upshift you just let off the gas slightly while lightly pushing the shifter out of the gear you are in. This breaks the torque on the gears and allows them to disengage without contact. Then when the motor winds down to the point where it sounds like the right RPM for the next gear, you lightly shove the shifter into that gear, and it will drop in without grinding. With practice, you can do it all in one smooth sequence, and go directly out of one gear and into the next without any hesitation.
Downshift float is a litlle trickier, assuming you are decellerating, you have to give it a little gas to break gear torque, opposite of upshifting, and then move the shifter out of gear. Then the RPMs must be brought UP to the correct speed for the lower gear. This can be a real trick, especially on real quick revving motors like Hondas. Most times I overshoot that RPM faster than I move the shifter.
Applying a very light pressure to the stick towards the intended gear can help, you can actually feel the gear drag decreasing until it meshes with the input gear, at which point it will drop in easily.
You feel the change in resistance just as the two synch up, then you stab it. This wears parts a little though, and should only be done until you get a feel for the right point to engage. Like he said, borrow someone else's car and practice
