I am deeply interested in Finance and the mathematics which forms the backbone. I get a lot of questions from juniors, batchmates about finance and how an undergraduate in engineering should expose him/her to the field of Finance. I think first, your decision in taking Finance as a future career option should be holistic and well thought off. With good mathematical background Finance seems easy to most of the IITians but trust me, the job requires a lot of hard work and time. Once entering a financial firm, dont expect that you will have a lot of time to waste around. Remember the famous quote:

"Finance, like time, devours its own children." - Honore de Balzac

So my suggestions to undergraduates (not pursuing finance as their academic major) on how to learn more about Finance and the world of Finance:

a). Start reading newspapers (ET, etc), magazines (BT, BW, Money, etc) for more business and finance news.
b). Visit some websites regularly Bloomberg, Yahoo Finance!, Google Finance, etc for latest updates and news.
When the above news and articles start making sense and ringing some bells in your mind, you can look forward to some formal knowledge in the field of finance.

A good starting point is to write a few NCFM's. You can learn more about NCFM's at their official page. NCFM's show a bleak interest in the field of Finance and basic understanding of the market instruments.

After writing a few NCFM examinations you will get a feel for the field and you should be clear in your mind whether you want to continue the field now or later (maybe in a few years).

If you wish to show serious inclination towards the field of finance you can write some of the professional financial examinations. You can choose between the following examinations: a) Actuaries: These are highly mathematics intensive examinations which test your understanding, agility and comfort level with mathematics. They are highly correlated with work done at insurance firms. These are very high demand high return jobs. You can ask Karthik Raman (a friend of mine) more about them.

b) Financial Risk Manangement (FRM): I cleared FRM in 2008 and I think I can give you the "been there done that" knowledge for these. FRM is conducted by GARP and is an international examination. Here is the official link. I also write a professional blog with a few seniors on more about the exam. Find the blog here.

c) CFA: CFA is the most celebrated and most popular financial examination at this level. Although not as mathematical as FRM, it certainly has a lot more value than FRM and is a good option at undergraduate level.

Feel free to write me an email for any further queries.