To get a seat in good Colleges such as IIT,NIT OR BITS You need to appear for Entrance exams, There is a common exam organised for IIT and NIT called Join Entrance exam, For NITs You need to get GOOD rank in JEE Main, which is held twice a year, one in the Month of January and other in the Month of April, You can appear for any or Both of the best of two will be counted for rank,when You qualify JEE  main You get a chance to appear for JEE Advance and those who get very good rank in JEE Advance get a seat in IIT.

For Private Institutes BITS and VIT and other they organise their own entrance exams, Those  students who get very good rank in Entrance exam are able to get CSE, 

Here are some reference links attached for various exams You can follow them

For JEE Main:

https://engineering.careers360.com/exams/jee-main

For JEE Advance:

https://engineering.careers360.com/exams/jee-advanced

For BITSAT:

https://www.careers360.com/exams/bitsat

For VIT:

https://www.careers360.com/university/vellore-institute-of-technology-vellore