Swedish has three translations for ”think”: tycka, tänka and tro, and the difference between them is often a challenge for learners. But that also means that there are many explanations online. These are sort of the core meanings:

tro = believe:

• ”Jag tror på Gud.” (I believe in God).

• ”Jag tror (att) han kommer klockan tre.” (I think he will come at three o’clock.)

tycka = have an opinion:

• ”Jag tycker (att) du är söt.” (I think you’re cute.)

• ”Jag tycker (att) du ska skaffa ett jobb.” (I think you should get a job.)

tänka = think about, imagine, use one’s brain, have mental images in your head:

• ”Jag tänker på min mormor ibland.” = I sometimes think of my grandmother.

• ”Jag kan svara om jag får tänka lite först.” = I can answer if I’m allowed to think about it first.

In addition to these, the particle verb tycka om (always with om and the stress on that word) means ”to like”, and tänka can also mean ”to intend” and is used when you talk about planned events that are going to happen in the future.

• Jag tycker om päron. (I like pears.)

• Jag tänker åka till Spanien i sommar. (I’m going to Spain this summer.)

I know it is probably wayyyy too late, but I found a great video explaining it here: https://www.youtube.com/watch?v=u7BEWUw9aCo&t=343s

hope it helps someone.

The subject forms are du and ni.
dig and er are object forms.

So we say Jag ser dig and Jag ser er 'I see you'
but Du ser mig and Ni ser mig for 'You see me'

In English, they're all the same, but if you try we instead, you wouldn't say What are us thinking about for the same reason.

Tänker is in the present tense and tänka is in the infinitive.