Admission in Stanford ,Harvard , MIT or other Top of the line Universities
According to my experience :
1.All require GRE subject Test. Some claim that it is not needed but in order that your application stands out I recommend you take GRE subject Test. This will facilitate a decision in your favor.
2.They need some research work. Preferably published individually or jointly with a professor. You may even have some peer reviews. People plan this well in advance and somehow wriggle through and get their name inserted along with a professor.
3.Your field of interest should match with a professor willing to accept you.
7.Good GRE and TOEFL scores
8.And above all apply early.
All or some of these come to play to decide on your application. And above all pray. There is nothing to beat luck.
If you are admitted by these institutes than financing your education will not be a problem.