Hi, Beth!
Among them, 认为and觉得are the most common words to say 'think' in Chinese. It's just that 认为 is more formal and cultivated than觉得.觉得is often used orally.
I think knowing these two expressions is quite adequate for your daily language use when it comes to 'I think, I believe, I guess, I suppose...', both spoken and written.
以为can be translated as 'thought' actually. e.g. I thought you were coming, but you didn't.我以为你会来.但是却没有.
我以为你不来了. It means that you thought the person wouldn't come, but he did come. e.g.我以为Beth是美国人,其实她是英国人.
想is a rather too commonly used verb, which has many meanings. To name a few: think, suppose, remember, reckon, figure out, desire, and even 'would love to'. It could be one of the most commonly used verbs in Chinese, too huge a topic, so I really suggest you looking this verb up in a dictionary for your own better understanding. For example, from my dictionary, a very big one, 想takes up an entire page, front and back! What can I say? Words like 想 in Chinese could be very reproductive. It's like the origin where many thinking words came from.
看as a verb basically means look, watch, and read, images you receive with eyes. However some phrases like在我看来has something to do with thinking, which can be directly translated as 'from my eyes, from my point of view, as far as I'm concerned, etc'. So, it is not advisable to regard '看' as 'think', because iIt could be confusing somtimes.
思考is to ponder, a kind of deep thinking, like meditation, thinking about very intricate things. e.g. 王教授正在思考.
想像, the word for 'imagine, or imagination' in Chinese. I don't think this word needs too much explanation.
设法is not think actually, it means 'manage to do, try to do'. I think the expression of 设法is very similar to the English one of 'make efforts to', because 设here means 'set up'----make, and 法means 'methods, ways, approches'----efforts.
Clearer now? Hope it helps :)