You are definitely good to go by about 1700, and pretty much completely lost before 1400 without special study. But it's hard to pick an exact date in between. It would be harder to understand the further back you go. Easier the later you go. Depends a bit on how good you are with modern English dialects, etc.

To start with, let's talk about Old English. Old English, aka Anglo Saxon, covers the period until 1066, and the most famous surviving text is Beowulf. It looks like this:

Hƿæt! ƿē Gār-Dena in ġeār-dagum,

þēod-cyninga, þrym ġefrūnon,

hū ðā æþelingas ellen fremedon.

Most modern English speakers find Beowulf pretty much completely baffling. Letters like þ are completely foreign to modern speakers. Even if they hear it rather than trying to read it, it's hard to spot much that is familiar. Plurals aren't formed by adding -s at the end. Word order is different (sentence ends in a verb). Grammar is different with cases. This language works a lot like modern German. But there are a few nuggets that are related to modern words if you know what to look for. Take that word cyninga. That's a plural - remember plurals don't get formed with s yet. So, drop off the a at the end and you get cyning. Still pretty strange. But spelling was less consistent then, and spelling rules change over time. C was a hard sound, so let's respell slightly clearer but mostly keep the pronunciation - kining. Just kind of mumble when you say it, and you get the modern word "king" with a syllable dropped off.

So, with Old English, you can find modern words hiding, but it's a lot of work to figure them, out.

In 1066, the Normans invaded England. They were from France, and spoke French. The french they spoke was not the same as modern French that you would learn in school. But it was closely related in many ways. With French speakers in control of England, french words and grammar started mixing with English, and it started to sound less like German. We call this phase of English Middle English. The best known work from this period is Chaucer's Canterbury tales from the late 1300's, so let's see if that looks more obvious than Beowulf did. You can see a mixed original + translation version of one of the stories online here: https://sites.fas.harvard.edu/~chaucer/teachslf/milt-par.htm

In one of the funnier passages of The Miller's Tale, you can get a sense of both the language and the humor of the time. Absolon has been annoying Allison. He's in love with her, and he shows up at her window and asks for a kiss. She's busy with her true love, so she pranks Absolon through the window and says he can kiss her. Try to pronounce it out loud. The writing uses modern letters, so you can get pretty close pronunciation without special training. But the spelling is still very old fashioned, so a modern English speaker may not recognize many words just by looking at them.

This Absolon gan wype his mouth ful drie.

Derk was the nyght as pich, or as the cole,

And at the wyndow out she putte hir hole,

And Absolon, hym fil no bet ne wers,

But with his mouth he kiste hir naked ers

Ful savourly, er he were war of this.

Abak he stirte, and thoughte it was amys,

For wel he wiste a womman hath no berd.

He felte a thyng al rough and long yherd,

And seyde, "Fy! allas! what have I do?"

"Tehee!" quod she, and clapte the wyndow to,

And Absolon gooth forth a sory pas.

Far easier to read! But still clearly not modern English. In particular, I lied to you a bit about how good your pronunciation was going to be because this passage was written before The Great Vowel Shift. But you can recognise a lot. "Derk was the nyght" is "Dark was the night" or "The night was dark." And "But with his mouth he kiste hir naked ers" makes sense if you pronounce it out loud. "Kistse" is now "kissed." "Hir" is now written "her." And "Ers" is the same word as the British word "arse." But something like "Tehee" could com straight from a modern text message. Here's a performer doing the same passage so you can hear it in a reconstruction of the original pronunciation: https://youtu.be/-EOkiGbgSlU?t=1676

Which leads us to 1400 and the start of the Great Vowel Shift. English changed quite a bit in the next few Centuries after Chaucer was writing, and by the 1500's, Shakespeare was writing in Early Modern English rather than Middle English. But vowels were still shifting, so not everything would be immediately familiar at this stage. Shakespearian English does have a lot of modern features. For example, plurals words are usually made with an s at the end at this point. Here's an actor doing a passage from Hamlet in reconstructed accent: https://www.youtube.com/watch?v=qYiYd9RcK5M

"Sea" still sounds like "say" because e's still sounded a lot like they do in modern German. "Sleep" sounds like "Slepp" because a written doubled vowel still just meant to hold the sound longer rather a completely different sound. And in particular, the first vowel sound in "heartache" still sounds a lot like the vowel sound in sea. A lot of our modern spellings date back to before the Vowel Shift when there was more of a 1:1 correlation between pronunciation and spelling. In a lot of cases, we've kept spellings from the earlier period even though the pronunciation changed like with sea and heartache.

By the 1700's, we have pretty much got modern words and grammar. There's no longer "thee and thou." Most of the unfamiliar features of the language are gone. It's just down to some old fashioned word choice and a slightly odd accent. Here's a clip from a film with a decent version of what American colonists would have sounded like in the late 1700's and really there's nothing that needs to be explained: https://www.youtube.com/watch?v=TGw9CXM6nqU There are some spelling reforms that happen after this point in American English, and writing rules change the way commas are used, etc. But it's pretty minor stuff.

So, if you pop out your time machine in the 1700's and order a drink, you are probably fine. If you crank it back to the 1600's, it's likely they'll think you sound real weird and don't talk properly. In the 1500's, you can definitely establish communication with a bit of work but you'll need to be quite careful with grammar and word choice if you want to be understood. In the 1400's or earlier, you really want to take a class before you time travel.