Generally B.Ed exam domains are the state governing body. For different state procedure might vary, but they all represent the same thing. Generally the application process begins in the month of feb- April while exam is scheduled for the month of May - June. After getting a good rank the university will ask you to set all the available college in priority basis. Depending upon your rank, you'll get a college through the priority basis. Otherwise you can do it through a private college that might cost you more.
Even though the tuition fee remains same in all govt. colleges, the caution money might vary. But at most you can through the whole 2 years costing you around 20,000-25,000.
To be eligible for this exam, you must have passed from any graduation college(10+2+3) approved by the govt. with a percentage more than 50%.
If you've done Btech in engineering with science or mathematics as base departments you need to score more than 55% here.
For SC/ST/EBC/OBC / differently abled students there might be a 5% relaxation for applying exam results in most of the states as per their state board rules.