In Episode 138 of Easy German at approximately 5:40, the guest speaker says, "Ich wusste nicht, wie die Grammatik zu lernen...", but the subtitles say, "Ich wusste nicht, wie die Grammatik zu lernen (ist)...", as if he missed the word "ist". Should that word be there? If so, please explain.
I watched the video and the guest speaker is not a native speaker. Some of his sentences are grammatically wrong or at least they sound unnatural.
Ich wusste nicht, wie die Grammatik zu lernen und dann hab ich einfach gedacht... (5:40)
is wrong. They tried to correct the sentence by adding the ist:
Ich wusste nicht, wie die Grammatik zu lernen (ist) ...
As a nativ, I still would reformulate the entire sentence, but with ist it is at least not wrong anymore. So the words in the brackets are corrections that can be easily be made while keeping the transkript as similar to the spoken words as possible.
There are definitely more errors in his German sentences, but most of them can not be easily corrected!
Well, even if the guest speaker doesn't say it (while he should), it's only one part of a video course and it's not a big deal to exclusively get referred to; in Extra video course also you see some mismatches, because written language and speaking language are not necessarily the same, in written language you must write just correctly and precisely, but in spoken language you can skip or shorten some vocabularies because of talking fast.
Secondly, you must know that some conjunctions like "wie", "weil", "bevor", "dass", "als", etc make the second clause (after the comma and one of these conjunctions) as subordinate clause! In this case, it's a subordinate clause (Nebensätze), so the auxiliary verb should be at the end. For example:
Es ist nicht Fakt, dass Deutsch leicht zu lernen ist!
Here you can see list of conjunctions that make subordinate clause with example and definition.