I am trying to understand the differences between the three (de) in Chinese.
let me answer the question you asked:
Firstly, I assume you are an English speaker.
的,地 and 得 are three very basic linking words in Chinese.
'的' is used follows attributes which are the adjectives you called.
She is a lovely girl.
她 是 一位 漂亮的 女孩。
So, you can notice that 'lovely' substituted by '漂亮的' in Chinese.
'地' is used follows attributes as adverbs.
He drives carefully.
他 小心地 开车。
The 'carefully' is replaced by '小心地'
'得' often express the meaning of degree and possibility. It is very complex to use and even the native speaker can make a fault.
Considering you are a learner, I recommend you to memorize this structure:
verb + 得 + a sentence
in the structure above, 得 is very similar to 'so that'
I'm so tired that I can't walk anymore.
我 累得 走不动路了
It linked the relationship between 'can't walk anymore' and 'tired'.
It can also express the possibility:
The floor needs mopping.
地板 得 拖了
In another word, 得 can replace 'need' and this a very idiomatic Chinese phraseology. I highly recommend you to replace '需要' terms of '得' in oral Chinese.
If you keep any questions, just ask. I'm very glad to help you.