I wish to appear in GATE, Can anybody suggest if I should go for some coaching or study by myself, and if so , how should I start?

you can decide by taking an online test for it....if you score good marks there is need for you to join the clases and if your marks are not so good you can join the clases
Now if you want to prepare by yourself ....First of all you should be clear in the mathematics subject...Practice is required for this subject...
Try and improve your APTITUDE ....as it is common part of any enterance exam you appear
Your basic and fundamental of all your core field subject should be clear

Now you can issue any GATE book from library and daily spend 1.5-2 hours solving the question.
After every 2 weeks give the online test and check your growth