I gather this is largely about spoken English so I will focus on that.
Long time ago, one of our teachers played us an audio version of the General Prologue to Canterbury Tales, in a reconstructed pronunciation. It was from a tape then, but similar versions are available around the net now. Here's one.
Even dipping one's nose into a facsimile of the Prologue leaves one unprepared for this, I'm afraid. The vowels and the consonants, not to mention the basis of articulation, are quite different from what we are used to today.
Canterbury Tales were written in the southern dialect (between ca. 1380 and 1400), i.e., in the dialect from which modern standard English largely evolved. Parallel to Cantebury Tales in the south, one may look at the poems of the Pearl Manuscript. Here is a transcription of Pearl, section 1 (it is admittedly alliterative, which may be occlusive; a normal chat would not be so), in the Northumbrian dialect. (Cf. the Wikipedia entry for 14th century Middle English.)
All in all, I think, one would have a great lot of trouble understanding, or makine oneself understood, around AD 1400. (With marginally better chances in the south, perhaps, unless one is akin to the northern dialects of today, language-wise.)
Even in Elizabethan England, pronunciation (of vowels especially) would take us by surprise, as the vowel shift was still taking place by then. (Again we're talking south of England.) Not to mention the vocabulary.
By way of an example, we recently had a question here at ELU on Adam lay ybounden, a 15th century English carol.
By and large, I believe up to three hundred years back would land one in a setting where one might make oneself basically understood, as to pronunciation and vocabulary.