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While nk attests to the Low German origin, the initial t must be due to influence by some inherited cognate. This is probably either tycka(“to have an opinion”) or Old Swedish þækkia(“to seem, think”).
to think(think to oneself, have a thought (process) in one's head)
Vad tänker du på?
What are you thinking about?
Jag satt där och tänkte på vad som hade hänt igår.
I sat there and thought about what had happened yesterday.
När jag hörde det så tänkte jag genast att det inte skulle fungera, men jag sa ingenting.
When I heard it, I immediately thought that it wouldn't work, but I didn't say anything. ("... så tyckte jag genast ..." instead corresponds to "... I immediately was of the opinion that it wouldn't work," which is a less common way to phrase it)
tänka länge och väl.
think long and hard.
(expressing sudden or intense thought) to think(hard, in order to solve a problem or the like)
Vilken finurlig och praktisk lösning! Här har någon tänkt till.
What a clever and practical solution! Someone has thought hard about this.
Den här olyckan får förhoppningsvis många att tänka till och ta det försiktigare
This accident will hopefully make many people think and be more careful
Jag skulle aldrig någonsin kunna tänka mig att måla huset i en sådan knallrosa färg!
I could never consider painting the house in such a sharp pink color!
Usage notes
For think in the sense of "be of the opinion," see tycka. Compare:
Jag tänker att pizza är gott.(an unusual thing to say in Swedish)
I think: "Pizza is good." / I think to myself that pizza is good.
Jag tycker att pizza är gott.(the natural way to say it)
I think pizza is good.
For think in the sense of "believe," see tro. Compare:
Jag tänker att filmen börjar klockan åtta.(an unusual thing to say in Swedish, though it might appear in a line of reasoning or the like, similar to "Here's what I'm thinking")
I think: "The movie starts at eight o'clock." / I think to myself that the movie starts at eight o'clock.
Jag tror att filmen börjar klockan åtta.(the natural way to say it)
I think the movie starts at eight o'clock.
Regarding the sense of "to intend" or "to mean", tänka is the main option signifying a setup plan, while mena (somewhat more colloquial) signifies what are the immediate consequences. For example: "I didn't mean to knock your teeth out" = "Jag menade inte att slå ut dina tänder" (or, alternatively, "Det var inte meningen att slå ut dina tänder"). Here, a translation with tänka ("Jag tänkte inte ...") may give the impression of "I didn't plan to knock out your teeth."