If you are seeking an internship in the finance industry then there is a high probability that you are a college student. If this is true then you already have one foot in the door because there is a chance that you have already learned quite a few of the basics of the finance industry so you will have no problem in an internship position.
You need to decide whether or not you want an unpaid or paid internship. Paid is great, but if you are in college then you need both the experience and the credits, so unpaid should work for your purpose. Remember if you do well and graduate then there will be plenty of time for making money later. If the company does choose to pay you for your efforts though, then you definitely have a good thing going that you should hold on to.
You need to make a resume, this is very important when searching for an internship because you want potential employers to see what you're made of and what you are capable of in a professional environment. If you need help making a resume, then there are probably services at your college or university that exist just for this purpose. Look around and see if you can find someone that can help you build the perfect resume so that you can attract the right employers.
If there is a finance club at your college or university then it would not be a bad idea to join it even if you are not big on the whole social thing. Sometimes employers will recruit members out of these financial clubs, meaning that every time you go it could be a job interview that you don't even know about.
If you do happen to land an interview, remember it is the same as a job interview even if it does happen to be for an internship, dress professionally and bring everything that you need, and you should be able to succeed.
