To become a fluent English speaker, you must study and master reading, listening, and speaking.
Some methods :-
1.Don't study grammar too much- Studying grammar will slow you down and confuse you. You will think about the rules when creating sentences instead of naturally saying a sentence like a native.
2.Learn and study phrases and collocation- These are essential part of spoken English.If you know thousand words, you might not be able to say one correct sentence. But if you know one phrase, you can make hundreds of correct sentences and similarly a collocation shows your level and knowledge of the language.
3.Practice speaking- In order to speak English fluently, you need to practice speaking.Practice speaking until your mouth and brain can do it without any effort. By doing so, you will be able to speak English fluently.
NOTE-->When you want to create an English sentence, do not translate the words from your Mother tongue. The order of words is probably completely different and you will be both slow and incorrect by doing this. Instead, learn phrases and sentences so you don't have to think about the words you are saying. It should be automatic.
4.Study correct material- You should read a newspaper daily (English). You can read novels,classical works and articles on different topics on internet.
You can also read magazines and comics.
5.Watch English news channels-As you are from India and you will be talking to Indians only,the Hollywood movies will not benefit you much as they are American(generally) and this will cause problem due to difference in accent.So it's better to watch English news channels as they use the same dialect as used in India and it will also help in increasing your knowledge and you will stay updated about current affairs.
You should also watch English Talk shows as they help in quickly developing communication skills,improve non-verbal skills and up-to some extent in grooming body language.
List of some books which will help you in improving:-
1.Cambridge - English Vocabulary in Use(upper-intermediate & advanced) by McCarthy and felicity O'Dell
2.Word Power Made Easy by Norman Lewis
3.Cambridge International Dictionary of Phrasal Verbs
4.Wings of Fire by Dr. APJ Abdul Kalam
5.I, Robot by Isaac Asimov