1. Sleep well. Run. IIT-jee is not more important than your health. Maintaining physical fitness can actually boost your attention span and concentration.
2. Listen to your teachers. Don't be an asshole. If you think your teacher is wrong, try to find a good reason why.
3. You will have doubts due to many reasons. Never hesitate to ask your teacher before your friend. Trust me on this. Teachers are much more wiser in explaining things to you. If your teacher tells you something and you didn't understand it, ask him/her again. They will be pleased to know that atleast someone is trying to understand the lecture. However, don't overdo it. Also, it will be helpful to the shy people.
4. When you see a problem, don't be scared of it. Sometimes you may feel like the syllabus is overwhelmingly massive, and you are lagging behind, but you gotta try and be rational. Just because the problem is from Maths/Physics it doesn't mean you cannot solve it using Physics/Chemistry. Maths and Chemistry bear no good relationship.
5. Learn to read. Do not wait for your teacher to finish/start the lesson or give you homework.
6. There is no point in doing the assignments after the due date. The reason is simple. The assigments that teachers give you is to check your understanding. If you don't do those problems in time, you will miss the discussions, the most important thing that coaching institutes offer you.

What is the point of giving an exam?

1. Check your understanding. Try to solve the questions you couldn't solve during the exam. I know this part is neglected by almost everyone even though its important.
2. See where you stand among your competetors.

Do smart people have a better chance to get into IIT?

On the contrary, smart people generally lack the motivation and the attention span to concentrate on studying. They easily get bored. So, No.

Are IITans smart?

Some of them are really smart. Most of them are ordinary. Some are dumb. On average, their IQ is above average. So, most of them just worked really hard. If you take an IQ test and it tells you that you are average or below average, don't worry because IQ is variable. If it tells you you are smart, don't take it for granted. According to the stats, there is a 50% increase in Problem solving ability when students were tested both in their 11th and 12th grades.

Tips/suggestions :

1. Don't do bulk-study. It is always important to maintain a diversity in what you study. Studying everything at once might seem helpful intitially but in the long run it doesn't prove very useful in retaining information. Also, don't study for more than 2 hours at once. Get up and have a cookie.
2. Give yourself a break. Have a day-off once in a while. Read a book or watch a couple of movies. Just don't overdo it.
3. Sleep for atleast 6 hours before any exam. I'd say sleep for 7-8 hrs. Don't stay up all night studying for an exam. Never do that. You'll probably fall asleep during the exam, or lose concentration.
4. Don't use many books. Get a couple of good books for each subject. For other references use the internet. It is better you buy a book that yor teacher prescribes because you always wanna buy a book that your teacher is comfortable with so that he/she can illustrate the concepts to you with ease.
5. Always study before giving a test, be it 15 mins for each subject, but do study. What I mean is you gotta prepare, to some extent, for every test. You have to make a conscious effort without taking for granted everything you already know.
6. Read NCERT books as many times as possible. Try to remember as much of it as possible. Prepare well for your Board exams.
7. Don't be intimidated by your competetors. Everybody makes mistakes.
8. Always solve a problem even when you know how to solve it. There is a probability that you are wrong or that you have found a new way to solve it.

Finally, be wise and have fun.

The important topics you are supposed to give special attention are as follows:
1. Maths
2. Physics
3. Chemistry

It is not important to do 12th class syllabus in 11th. In your summer-break just try to finish 11th. Revision periods would be sundays. If you are a christian and gotta go to church and all, it is better you start on saturday and revise everything you've learned that week.

This is neither a recipe to qualify in IITjee nor the things you are supposed to do. These are just the things I learned during my preparation; things I wish I had known as a beginner. I wish you all the best.