1. What is the ideal time to start applying for internships?

It would be ideal to start sending out resumes from the first career fair that is held at the university, sometime in October.

2. How useful are the career fairs at Columbia?

For CS  : Some very good companies come to the career fairs at Columbia and almost all the known or sought after companies hold a tech session at the University. Google, Facebook, VMWare, almost all the major finance companies like Goldman Sachs, Bloomberg, Morgan Stanley etc hold tech sessions or are a part of the career fair. There are start-up career fairs too where you find companies like Tumblr, Knewton, Yodle etc.

For OR : There are few finance firms that turn up at Career fair and most of them have IT/CS openings. There are plenty of jobs available for Analytics and mostly all finance firms will have an opening regarding the same. So, I think it would be wise and very useful to invest time at Career fair.

3. What are the most sought after skills in a summer internship for CS?

Most of the interviews are based on Algorithms, and projects that you have worked on. The programming questions are generally on the lines of the questions in the books Cracking the code Interview and Programming Interviews exposed. Going through these books should give you a general idea about the kind of questions asked.

4. What are the most sought after skills in a summer internship for OR?

For Finance, you need to be really good at C++/C if you targeting Quant roles, For analytics, you need to be good at SAS, R, MATLAB. Python is a big plus. SQL, EXCEL is mandatory. It really helps you to find jobs. As far as programming experience is concerned, it is a big bonus if you are hacker being in OR. It will land you up with a very good job.