Through JEE mains first you go in for the main exam where you appear for the exam you wait out the result if you cross the cutoff you will definitely get a college on the basis of your main score but you will also get the chance if you clear the cutoff to get into giving the advance paper , advance paper if cleared will get you the option of IIT and NIT these will be given to you by the authority that is the JOSAA. You will go through a few rounds of counselling after which you will be allocated your college based on your rank in JEE advanced paper or in the mains paper as well and then you could easily apply for it or not apply for it and wait out the other examinations you would have applied for also you have the option of category rank category rank evaluation that is the extra round of counselling where people on the basis of their category would get a better college than they would normally.
The expected cutoff for mains is:
Gen 81
Obc NCL 49
Sc 32
St 27