I would sum the 3 essentials to succeed at IIT-JEE or AIEEE as
 

1. The right study material
2. Hard Work
3. The desire to succeed

Let me clarify in the very beginning that the 3 essentials highlighted here are no magical tricks or tips that will help you crack IIT-JEE or AIEEE. This article is meant to clear the clutter or misconceptions in the minds of students as well as their parents. There is no short cut to IIT-JEE or AIEEE for that matter.

The Right Study Material
School Text Books Are Enough
There are umpteen number of books which one can read to prepare for IIT-JEE. A concise list of books is provided here.
Since a student does not have unlimited time to prepare for IIT-JEE, he / she cannot study so many books. A student gets two attempts to appear for IIT-JEE; that too in two consecutive years. There is also an age limit. Ideally, one gets 2 or at most 3 years to prepare for IIT-JEE, during his / her class 11th and 12th.
Most Education Boards in the country have an extensive syllabus in these classes which more or less covers the entire syllabus for IIT-JEE or AIEEE. Books published by NCERT are written by a team of well qualified experts on the subject. These are one of the best text books I have come across. Students aspiring for IIT-JEE should study these text books thoroughly during their Class 11th and 12th, to get their concepts in place. Other than these, students should take up a good correspondence course.
A Good Correspondence Course
Some of the good correspondence courses or distance learning courses are provided by Vidyamandir Classes, Brilliant Tutorials, MissionIIT etc.  Distance learning Pack by MissionIIT is one very good package available.
These correspondence courses cover the entire syllabus for IIT-JEE and AIEEE. They do not delve much into theory and are divided into 3 sections
Chapter Summary / Fundamentals
Solved Examples
Practice Exercises
Most Correspondence Courses also offer a Test Series. The Distance Learning Pack by MissionIIT offers an Online Test Series. These tests are conducted every 2 months based on the chapters covered till date. Test Series drill the students under simulated IIT-JEE conditions and also provide rankings on a state and country levels. Since these tests are taken by thousands of aspirants all over the country, these give the students an evaluation of their preparation levels.

Hard Work
I would have called this Smart Work but I fear being misunderstood for suggesting unfair means or some tips or tricks. But believe me, none of the usual smart works work in IIT-JEE.
I have come across some parents and teachers who suggest studying for 18 hours a day for 2 years. This sounds impossible. If an aspirant studies for 4-5 hours everyday, but on a regular basis, I feel he should do well in IIT-JEE and AIEEE. But this 4-5 hours study is to be done with full concentration and on a regular basis. This study time does not include the time spent at coaching institutes. This is dedicated self study; with a pen in hand; solving problems.
Coaching, Coaching and Coaching
Some parents believe in keeping the students occupied with one coaching or the other. The student attends one coaching institute on MWF (Monday, Wednesday, Friday)  and another on TTS (Tuesday, Thursday, Saturday). Besides this the student has a home tutor to help him / her prepare for Board Exams. There could not be anything worse than this.
Coaching is meant for guidance.
After the coaching class, the student should be studying the topic on his own and solving problems for gaining proficiency. But with coaching after coaching, there is hardly any time left with the student. So he performs miserably in his school exams as well as in IIT-JEE / AIEEE. The parents put the blame on the coaching institute and the teachers.
IIT-JEE is all about intelligence. An aspirant needs to sharpen his problem solving skills to be succesful at IIT-JEE. No coaching institute can instill these skills in a student if he himself is not putting in sufficient practice.

The desire to succeed
Call this Positive Outlook or Positive Thinking or Being Ambitious; but without dreaming big one cannot succeed. Mahatma Gandhi once said "A man is but the product of his thoughts. What he thinks, he becomes. "

NO

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Success in exams like IIT-JEE / AIEEE depends on ones ability to solve problems based on applications of theory taught in Class 11th and 12th.
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Those aspiring for IIT should have clear concepts and ability to visualise. To break up the problem into distinct sub-parts.
Above all, one needs the willingness and desire. The desire to achieve.
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In the last few years, coaching institutes have been offering courses that help students clear IIT-JEE.
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Most students take IIT-JEE in the same year that they appear for their Class 12th Board exams.
The coaching institutes typically have 2 year courses which start as soon as the students join 11th class and all the way till Class 12th.
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Imagine this scenario:
Vikram has cleared his Class 10th exams. At N D T Public School, Vikram is studying in Class 11th with PCM (Short for Physics, Chemistry Mathematics), the subjects necessary for those who want to appear for Engineering Entrance Exams. There are 2 such sections in Class 11th and the no of students in these two sections add up to 84.
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Almost all of these 84 students have joined one coaching institute or the other for preparing for IIT_JEE, AIEEE etc.
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These coaching institutes have classes thrice a week on alternate days; Monday-Wednesday-Friday OR Tuesday-Thursday-Saturday; normally called MWF and TTS respectively. Some have classes on weekends; Saturday and Sunday.
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Vikram's school gets over at 2:30 PM. His classes at the coaching institute begin at 3:30PM. So, Vikram has time just enough to run home, change his clothes, gulp down a few bites from the lunch his mother keeps ready for him and finally manage to reach his coaching classes.  
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After the hectic day at school and the marathon run to the coaching institute, most of the energy and concentration is drained.
Now in the classroom, his mind is wrestling to keep awake.
He barely manages to scribble in his note book, a few points from the lecture.
After a 15 minute break, the next class begins.
This session gets over at 6:45PM. Coming out from the class, he joins his friend for a plate of Chowmein. He is hungry because he couldn't finish his lunch at home.
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Reaching home by 7:45, he wants to watch the ending of the 20-20 between India and Australia.
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Vikram's mother serves dinner at 8:30 PM and by the time everyone gets over with dinner, he remembers that he has to complete his Physics Practicals Note Book.
Vikram meticulously completes his home work. By then, it is 11:30 PM and his father cajoles him to go to bed; after all he has to get up the next morning by 6:30 AM to get ready for school.
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One day is over.
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The week will get over in the same way.
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At weekends, he will have enough homework given by his school teachers to keep him busy.
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This routine will continue and by the time we realise, Vikram would be getting ready for his Annual exams of Class 11th. Since the result of this exam (Class 11th)  is more important, his coaching classes and preparation for IIT-JEE or AIEEE will take a back seat.
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Do you think he has prepared for IIT-JEE in any way?
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Now, picture this:

Vikram comes home from school.
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He has his lunch and finishes his homework.
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Then, Vikram has a short nap of about 30 minutes.
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When he gets up at 5:00PM. He is now ready to start studying for his target in life; IIT-JEE
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Vikram has enrolled for a Distance Learning Pack and they send him modules and practice questions every month. He reads the brief theory and basic concepts, practices the solved problems on his own and then attempts the exercises given for each module. They also conduct regular tests and give a detailed report about his performance. He gets to know his All India Rank based on these tests. So, he knows exactly how far he is from achieving his goal.
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This way he spends about an hour and a half on each of the 3 subjects - Physics, Chemistry and Mathematics. Almost 5 hours of dedicated study.
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His friend Kamal who lives a few blocks away is also preparing for IIT-JEE. He is also following the same routine.
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If Vikram has a problem with a topic, he discusses it with Kamal. And when Kamal has a problem, he discusses it with Vikram.
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This way, they both complement each other's learning.
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Vikram realises that if he studies well for IIT-JEE and AIEEE, he has also covered his school syllabus.
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Coaching for IIT-JEE has become more of a fashion. But it has a huge following.
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Everyone joins coaching for IIT-JEE, everyone appears for IIT-JEE and everyone hopes he will get a rank in IIT-JEE.
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All this without doing any serious study or hard work.
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Most parents believe that joining a coaching institute is a sure shot way to success in IIT-JEE.
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But it is not their fault too. The coaching institutes make such wonderful presentations that it is hard to disbelieve any of their assertions.
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To cut the long story short, There is no short cut to IIT-JEE.
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If your child is just spending time running from school to the coaching institute and from one subject tutor to another, then he is not going to make it to IIT-JEE. For that matter not even a good college through AIEEE.
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Simplify things for your child. Make him get into the habit of self study.
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And if this discipline cannot come to your child, forget dreaming of IIT-JEE.
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You will only be wasting your money paying fees to the tutors, coaching institutes and the cabwallah.
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