If you want to really see how close the relationship between the Germanic languages are, line up some sentences German, Norwegian (or Danish or Swedish), Dutch, English, Icelandic next to each other, and then a second group with Middle High German, Norse (for the modern Scandinavian languages), Old Dutch, Middle English, Icelandic.
Basically if you pick up any modern pair, you get a ton for free. Pick up a third, or even just learn a decent amount about one, and you start picking up a lot of patterns that lets you infer meanings. If any of the modern pairs includes Icelandic, you'll benefit strongly from knowing the older versions of the other one in the pair...
Learn the patterns of how newer forms of your own language derive from the older, and you'll find you'll start being able to "shift down, sideways and back up" very often.
E.g. Dutch or German sch => sk in the Scandinavian languages. "u" in middle of a word => "o". Hence "Schule" => "skole" (school). There's dozens of simple transliteration rules like that.
In terms of older forms, an example from Norwegian that illustrates the closer relationships, that I'm particularly fond of because it's an oddity, is "vel bekomme".
It is a pleasantry that basically means "you're welcome" specifically used after a meal. It's a fun one because while "vel" ("well") is still used in modern Norwegian in many contexts, including in e.g. "velkommen" (welcome), "bekomme" now doesn't even figure in most dictionaries on it's own, and some younger Norwegians would struggle to explain what the word means on its own (I'm 42, and my generation too rarely used it separate from the phrase "vel bekomme", but were quite likely to hear it in somewhat wider use in our childhood)
But it's the same word as German "bekommen" one of the meanings of which is for food to "agree" with you, and with etymology that converges with the etymology of English "become".
Which sounds weird until you deconstruct both into roughly a mix of "to take on" (characteristics of), "to receive" (well).
The fun thing is that when directly transliterating the words into the closest German/Dutch cognates, it's not perfect, but it's close enough that if you know the history of the words, it's becomes obvious in context.
At which point the other (archaic; you may still find old people use it, but even that is becoming rare) Norwegian use makes sense: "Det bekommer Dem" => literally "it becomes you" (in the meaning "it suits you")
For some younger Norwegian speakers, that latter Norwegian phrase is now so unusual that it's sometimes first when they learn German or learn the English phrase that the meaning fully "clicks".