How can I understand the basics of programming and learn programming in a very fast and easy manner?

Many of these answers provide some fantastic insight into developing one's coding skills. This is really what any web developer or programmer does essentially. Web and mobile design is a continuously developing and changing area, so there is always more to be discovered. That being said, there are some really excellent resources for working with many of the most common programming languages while also learning the basics of them. A few of my favourites include: http://Codecademy.com http://Nettuts.com http://Sitepoint.com http://Teamtreehouse.com http://SmashingMagazine.com Hope this helps without being redundant!

I think by more of practice and practice and practice solving problems, building systems, tools.

You really can't learn programming fast, it's something you'll always work at, but a good resource is http://thenewboston.com or thenewboston YouTube channel

Common man! Any body can learn programming with practice, debugging the errors and handling more features in that particular programming language.

Join edu2code dot com in Bangalore and you can further your programming skills. they have a 2 month Prep training.  It is an excellent team and you can get a very good experience.  It is in Bangalore hands on training.

It is nice idea to spend the vacation in an useful manner. C programming is a skill. You need to practice a lot. You can do it by yourself. Lot of web sites are there to help you. But if you have a Trainer/Coach then you can do better. As an Industry person I can help you to master your C programming skills.  I act as a Trainer while you are learning and I act as a coach after you have learnt.

I just wrote an expansive answer for a similar question, please check out : Shariq Shaikh shared an answer on Quora with you - My answer to How should I improve my Coding skills?

Learn basics of any popular programming language and start solving problems in Project Euler. https://projecteuler.net/

Trying a new language for just a 2.5 month vacation is pointless. Better to improve your C. You already know basics, and only you know what you are weak at. So I'd recommend to first perfect what you know (Practically) and then move on to advanced topics. There are many websites which give great tutorials on C. Though, I would recommend you to buy some good book , like "Keringhan and Richie's The C programming language". Even though there are only 2.5 months, it will be also of great help afterwards and I don't think it costs a lot. I don't know if you do this, but some people have habit of just reading the book, DON'T DO THIS, EVER. Try what you read practically atleast once