Verb + 起來

Can someone explain this in a simple way? The book I'm using didn't really explain it to my liking.

You can use it to show a fulfillment of an action:

想起來 = to think up (something)

包起來 = to wrap up (something)

When 起來 comes after a stative verb (a.k.a. adjective), it can be used to mean the onset and continuation of that state:

冷起來 = to get cold

It can also be used with "sense" verbs (to hear, to see, etc.) to indicate an impression of something:

聽起來他很高興 = He sounds very happy.

看起來沒問題 = It looks not to be a problem.

Yes, I know that I made that thread before, and I probably could have just upped that one, but they were 2 different questions. What Qilai means, and what it means after a verb.

I think you answered it well Claw, thanks. A question though

聽起來他很高興 = He sounds very happy.

看起來沒問題 = It looks not to be a problem.

in these situations, must the verb come first?

他聽起來很高興 or is this ok

in these situations, must the verb come first?

他聽起來很高興 or is this ok

I believe that should be fine.