te-form + ru (-てる)
You should all know what the te-form is. You should also all know what te-form + iru is. Now it’s not the farest fedge in the world, but te-form + ru is a frequent abbreviation of te-form + iru. It’s never short for te-form + aru or oku, just iru. So it points out that something’s on-going. 食べてる = I’m eating, 読んでる = I’m reading, yadayada. Simple stuff. You wanna remember this.
masu-form to connect sentences
You might’ve noticed that frequently there’s a masu form of something in front of a comma. Narration usually connects sentence in the sense of “and” by just wrapping it up with the masu-form. You gotta be a bit more careful with “shi” (し) as it can also connect “reasons,” yet it’s the masu-form of “suru” (する, to do), too. Though “shi” translates to “and” in any case. It might influence the nuance, though.
toku (とく) at the end of a verb
I think it practically comes down to masu-form + toku, but I’m not all too sure and tired, so let’s just say “toku at the end of a verb.” It’s the colloquial version of te-form + oku which has the nuance of doing something in preparation. “Oboetoke” (覚えとけ) would basically mean “better remember that!” as it’s in the command form, too. “Te” and “oku” are kind of a pain to pronounce so it became “toku” in colloquial speech. Just like “teru.” As a side note, I really think using te-form + oku yourself as someone from North America or Europe is pretty god damn hard since it seems utterly unnecessary in its function. I really don’t see where it’d ever come in handy, it appears expendable. But you gotta keep it in mind, at least.
(Note: I’ve found a very good and easy-to-understand example of when te-form + oku is actually a really handy construction to use after I’d written this post. 「言っておくけど、…」 – which basically translates to “I’ll say this just in case(/in advance), but…” Now you all know how this works. Hopefully. Though I’m still thinking that scratching this construction from the Japanese language wouldn’t make it harder to understand for anyone.)