How/When did English transform to the modern version we use today? [closed]

The short answer is: Always.

Languages evolve all the time, very gradualy, as usage changes, words fall out of favor, and new words get used that had never before existed. The fact that new words are added to dictionaries every year (and certain unused words are taken out) is a part of this, but more representative of the larger evolution that language undergoes.

And it is still happening today. You may complain about the words "twerk" and "selfie" being added to the Oxford English Dictionary, but formerly-slang words fall into common use all the time, and this will continue to go on for as long as the English Language (and languages in general) exists.

Letters are dropped for simplicity, new words are added to represent modern ideas, and they fall in and out of favor with English speakers. There is no one 'event' that caused this.

Also, if you think the shift from Shakespearian English is drastic, look at Beowulf, which literally requires a translation into modern English.