Firstly we have the national entrance examination for entering the NITs or IITs. To get to one of the NITs, you must have a good rank for your IIT JEE Mains and for getting into one of the IITs you need to get a good score for IIT JEE Advanced.
And we have many other state wise entrance exams like KEAM for Kerala.
And finally you have the exams conducted by private universities like VITEEE for getting into VIT.

After the ranks are published you go for counselling and get to choose the course based on the availability and your rank.
You could also get admissions through management seats which are usually more expensive but easier to get