I often have a problem understanding how Taiwanese think. So I decided to do a research and asked my wife to tell me which words or phrases, that express thinking, thoughts or ideas, exist in Mandarin. Below is a list with examples, which is narrowed down to the most important and common ones, that are used in daily life. There are many more words in Chinese, that express the same thing, but they are usually used in literary works or special circumstances. For a beginner student of Mandarin, these should suffice. You can use these phrases as a reference.
1. 想 xiǎng: to think, to want, to miss
想 is the most basic word one associates with thinking and thoughts. It's also used in combination with other words and helps to expand the meaning. See some examples below:
Ní xiǎng tài duō le.
You're thinking too much.
Wǒ xiáng nǐ.
I miss you.
Ní xiǎng shénme? Nǐ zài xiǎng shénme?
What's on your mind? What are you thinking now?
Wó xiǎng shueì jiào.
I want to sleep. (Lit. I'm thinking about sleeping)
Wó xiǎngyào chī shueí jiǎo.
I want to eat dumplings.
2. 想想 xiángxiǎng: to think
Xiángxiǎng qù nálǐ zóuzǒu?
Where would you like to go?
Ràng wǒ xiángxiǎng...
Let me think... (Used before thinking about something)
3. 想起 xiǎngqǐ: to think of, to call to mind
Wǒ xiángqǐ wǒde nǎinai.
My grandma comes to mind. (When talking about something, that reminds you)
4. 想出 xiǎngchū: to figure out, to think up
Wǒ xiǎngchū zhège diǎnzi.
I came up with this idea. (Lit. I thought out this idea).
5. 休想 xioūxiǎng: don't think about
Nǐ xioūxiǎng kàn diànshì!
Don't think about watching TV! (Much firmer as the similar 不要)
6. 認為 rènwéi: to think (indicating a direction)
認為 and 以為, both meaning "to think", are somewhat related, but they are usually used in different contexts. While 認為 indicates a positive note and a thought in a certain direction, 以為 is indicating a disappointment and usually an explanation or a "but" follows.
Wǒ rènwéi Táipěi hén hǎowán.
I think Taipei is really interesting.
7. 以為 yǐwéi: to think (indicating a disappointment)
Wǒ yǐwéi Táipěi hén hǎowán, dànshì méiyǒu.
I thought Taipei is really interesting, but it's not.
8. 惦記 diànjì: keep thinking, think a lot
Wǒ diànjì nǐ.
I think about you a lot. (More like: You are always on my mind.)
9. 考慮 kǎolǜ: to seriously consider something
Wǒ huì kǎolǜ.
I'm seriously considering it.
10. 花心思 huāxīnsi: to think thoroughly
Wó huāle hěn duō xīnsi tiāoxuǎn nǐde shēngrì lǐwù.
I spent a lot of time thinking about what to pick for your birthday gift.
11. 感到 gǎndào, 覺得 juéde: to feel, to sense, to think
感到 and 覺得 indicate a mix of inner feelings and thoughts, both are very similar in meaning.
Wǒ gǎndào/juéde nánguò.
I feel sad.
12. 念頭 niàntou, 點子 diǎnzi, 想法 xiángfǎ: idea, thought
Wǒ yóu xiǎng guàng yèshì de niàntou.
I have the idea to go to the night market.
Wó xiǎngchū zhège diǎnzi.
I came up with this idea.
Wó yǒu zhège xiángfǎ.
I came up with this idea.
Please note the rules of pronunciation in standard Chinese phonology. Two 3rd tones in a row make the first syllable become 2nd tone, for example: xiǎng + xiǎng = xiángxiǎng etc. Read more here.