To get an internship you first have to shortlist the department you are interested to join in.
Get the resume and cover letter ready as why are you suitable for an internship in that company and either you can go in person or apply online on their site.

If you don't get to meet the concerned person, hand over the resume and letter to a junior at HR and request him to forward it.

Also you can ask your friends and other references to help you to get in with or with/without pay and for good experience.

Most of the MNC's pay stipend to their interns if they have an intern requirement and if you have an interesting profile.

Hope this helps.