to think -- 想，感觉，觉得，以为，认为

There's actually a LOT of ways to express "think" in Chinese. There's also '看“, like in this sentence: 你看怎么样？(what do you think?) and 感觉(which is much like 觉得).

以为　means to "mistakenly think" something.　The same way in English when you say you *thought* something, it implies that what you were thinking is in fact not true. 我以为他没有女朋友－I thought he didn't have a girlfriend. [but he actually does].

认为 is more like "believe" as in "我认为很多人住美国，可是我没去过，这就是我的想像。(I believe many people live in America, but I haven't been there. This is just my thinking.) 想 has a few meanings: to think of someone/something, to think (contemplate), to want/would like to. It is like the desire of wanting to do something, but not necessarily meaning the action will happen: 我想出去外面，可是没什么打算。－I would like to go outside, but I don't have any plans. It also means 'to think', 我在想办法:I'm thinking of a method. 我想你 - I miss you. 想 is the most flexible out of all of them because it has so many meanings. 觉得 means "to think/feel." 我觉得她很可爱－　I think she is so cute[this is my opinion] 我觉得不舒服－ I don't feel well.

感觉 = feel or feeling 
我感觉不到它 = I can't feel it.
我感觉好点了 = i feel better.
不好的感觉 = bad feeling

感到 = feel or realize
我感到很抱歉 = I feel sorry. or I'm sorry.