I have worked at Microsoft, Google and Facebook as a software engineer, going through the full interview process every time.

The thing to realize is that being good at technical interviews (as done by the above companies) is a skill unto itself but it is a skill an intelligent person with a comp sci background has the ability to get significantly good at after a 1 to 2 months of disciplined preparation. - I went to a top ranked school myself and had a comp sci degree but was very intimidated by technical interviews until I realized that this was no different than all the other other intellectual hurdles/gauntlets I had successfully navigated up to that point by giving myself time to thoroughly prepare.

Get "Elements of Programming Interviews" and give yourself 2 months to prepare. Start to with "1-month" plan in the book spending at least an hour a day at the very minimum. (I have worked through both Elements of Programming Interviews and Cracking the Coding Interview in their entirety and while both are good, in my experience Elements of Programming Interviews was clearly the better preparation in terms of technical depth, breadth of exposure to the kinds of questions I faced in the full-day interviews, and succinctness of coding solutions)

Get dry-erase paper/notebook or a white-board and work through the problems by hand including the coding (important!). For the first week or two give yourself an honest focused couple of hours to wrestle with a problem before looking at the solution. it is not enough to settle for "I think I know how to solve this" - Actually code up the solution by hand and step through it with some simple cases. This is important and it allows you to develop confidence in your ability to think methodically through a problem as well as giving you an opportunity to develop mental heuristics for how to tackle and test unfamiliar problems. Developing confidence in your ability to think through interview-style problems is every bit as important as exposing yourself to interview-style problems. As you progress, you will be working towards being able to deconstruct a problem and be ready to start coding up a high confidence solution in 15 - 20 minutes.

"Talk to yourself" as you try to solve a problem to simulate explaining your thought process to someone as you go along.

When going through the solutions in the book, do not gloss over a detail you do not understand. Go online and find alternative explanations/references if you don't understand some detail of the solution provided.

After a few weeks of this kind of daily disciplined prep, you should start feeling pretty good and your confidence should start building nicely. Lots of interview questions are variants of each other and once you have enough breadth, you start quickly being able to key into the "type" of question and possible solution approaches almost as soon as you hear it.

Last thing is when you feel ready to start doing interviews, do not interview with your "top choice" first. If you can find someone that has done interviews to give you a mock interview, great! If not, schedule interviews whose outcome you are not as attached to (relatively speaking) first.

Hope that helped.