Certainly in other languages like my native Swedish, a negative is expressed with the verb followed by not.

Jag pratar inte Svenska = I speak not Swedish = I do not speak Swedish

In English, however, a negative is expressed in a very odd way.

I do not speak Swedish. 

The DO NOT seems to me, to be a double negative, and should cancel itself out to leave - I speak Swedish!

In older styles of English, certainly language around the time of Shakespeare, it was common to write: I **speak not**. I speak no. = I do not speak. 

How did the verb in bold evolve to the **I do not speak** construction that we use today?