"I have been trying to get an internship and the process has baffled me. People with contacts in big companies have an unfair advantage even though they are not that skilled. I tried to approach my alumni regarding referrals but to no avail."
No process of hiring is completely fair. That's the truth and the sooner you accept it the better you can prepare yourself.
Every organisation has its own recruitment process and it's wrong on your part to call everyone's process unfair. People with contacts in big companies do have advantage but I don't think that's unfair. They have devoted their time networking with employees of big companies.
Even though there are some people who get internships with contacts, BUT, let me tell you this:
No Big company will hire someone for the sole reason that they are recommended.
In case of jobs, the contacts can only take you up to the interview table, you have to prove yourself there.
There might be some exceptions where the recommendations work, but it is not significant in proportion.
Don't let that feeling depress you, and stop you from trying.
Remember, getting an internship is NOT the only thing that matters.
Those who get from recommendation and without talent would eventually find it too tough to bear, and would eventually drop off, or under-perform.
You can always get good internships, if you have a good enough profile, interesting skills and good commitment.
If you didn't get an internship somewhere, it means something else, something better is waiting for you.
Some people are lucky to have a close relative in a big company but in the long run your luck will help you also in some situations. So it's all even. Networking is essential to get good referrals.
Here are some tips you can follow to improve your networking skills:
Add good connections. Follow interesting people. Share your thoughts. Post useful comments on interesting post. Let people know you're there.
Hackernews, reddit, Quora, etc. Posting a good comment is great way to attract attention. You will get in touch with great people who may be able to help you out in future.
Attend onsite competitions.
Interact with people smarter than you. Learn from them.
Hangout on interesting IRC Chatrooms. Ask interesting questions.
So, getting a good internship is not based you don’t have someone who works in a Big company, is because you have to accept the fact that there might be this kind of “unfair” phenomenon. And all you have to do is better yourself, build up useful network, and perform well in the interview. Good luck!