Hi Yashanshi,

• if you wish to join Government Institute, then there is a lengthy procedure of application, interview and required eligibility criteria. For example Government Poly-technique Pune. And you can apply only against advertisement.
• If you wish to join private run Institute, but government recognized, a process is almost same, but you can directly apply. This is little easier. If your CV is compatible and suitable for CV. That is if you have B.E. in Mechanical and Institute runs mechanical/production/industrial Engineering as one of the course, then you are eligible. Simply apply to director or their placement department.  
• But best way to get into, is to find out if you know someone there. This person will be able to tell you, who is really "decision maker". In many Institute's directors is not the one who calls the shot. But someone representative of management who looks after the day-to-day affair. Also, your contact person will be able to tell you, is there a requirement of any faculty in that institute. Then go ahead and apply. I guess you are trying in Maharashtra, there are so many Institutes, I think this should not be very difficult to just list the Institutes, their directors, your contact person and start calling/connecting one by one.  Essentially networking is the key to get into right Institute.

You can try at totally private Institutes, this will be mostly their need-based and your merit or suitability for the job.