Things you should do:
1. Think SMOOTH, and be SMOOTH. This cannot be over-emphasized in a Viper (of any generation). Even with the best (and fresh) tires, setup, and so forth, the Viper does not respond well to sudden or abrupt inputs.This also means keeping your transitions from throttle to brake, and brake to throttle, smooth. The same goes for shifting, and steering.
2. Get everything warmed up before you drive the car hard; this means tires, brakes and engine. This is not only kinder to the driveline; as has been noted, cold tires and high hp/torque don't mix well. This is especially true in cool and/or damp conditions.
3. FOCUS! This car demands your full attention! The cockpit of a Viper is no place for woolgathering, yakking on a cell phone, or any other form of distracted/inattentive driving - PERIOD! On the street, be alert to the traffic around you; this makes it less likely you will have to do anything sudden (See no. 1)
4. Keep BOTH hands on the wheel except when shifting. The best time to adjust the a/c. radio, etc. is when you are stopped. Like any car with wide front tires, a Viper will bump steer and tramline (follow groves in the pavement). This may be disconcerting to newbies, but is not a serious problem, IF you are aware of it, and paying attention.
5. Work up to your personal limits in the car slowly and carefully; then, STAY WITHIN THEM. YOUR limits are THE limits (regardless of what the car will do)!
6. If you have not been to a high-performance driving course, GO TO ONE! At a minimum, go to an HPDE (or two, or three). Learn and practice your skills with the best guidance you can get, in a controlled environment.
7. PRACTICE, PRACTICE, PRACTICE! There is no such thing as too good, and ALL of us can improve. You can even do some of this on public roads (at a reasonable speed and with no traffic); practice heel and toe downshifting, driving the correct line through a corner, etc, until you can do it correctly, every time, without having to think about it.
Things you should NOT do:
1. Stab the throttle or brake. Squeeze it, DON'T slam it!
2. Turn into a corner too soon; this is called "early apex". It's a natural novice mistake. It's also the worst line through a turn, gets the car out of shape, and can lead to a spin, especially if your entry is too fast to begin with. The Viper's normal understeer is your friend here (at least while you're learning) as it tends to keep you from doing this.
3. Shift while turning; as has been noted, it unsettles the car.
4. Short shift (upshifting way below redline) under hard acceleration; this can cause snap oversteer. The same goes for quickly going to wide open throttle in a higher gear than necessary. This is the classic "Viper Bite", and the ONLY place you want to experience it is in a closed environment, like a big, empty parking lot or a skid pad, where you can't hit anything.
5. Show off - EVER! YOUR EGO IS NOT WORTH YOUR LIFE OR ANYONE ELSE'S, nor is it worth wrecking your Snake! The last place, THE VERY LAST PLACE, for demonstrating your machismo or bravado is behind the wheel of a Viper! Before you get in, strap in, shut the door, and push the start button, park your ego outside and leave it there, until you park the car and shut it off.
6. Street race - EVER! Keep the competition on the track, drag strip, or autocross course!
7. Assume that any tire, modification, or setup is a substitute for skill, experience, and sound judgment.