Part-of-speech problems about adjectives or adverbs preceding 地
Adjective is placed before noun and Adverb is placed before verb
So in your Context &quot;高兴/地/说&quot;, since 说 is a verb, 高兴地 will be an adverb.
高兴 itself can be a noun, adjective or adverb depending on the context and any preposition character following it.
的 is used before nouns , e.g. 灿烂的笑容 charming smile, it served as a possessive particle too
地 is used before verbs , e.g. 用力地踢 kick it hardly, 仔细地观察 observe carefully
得 is used before adjectives, the words before 得 are usually verbs. e.g. 扫得很干净 Sweep very clean, 做得很好 nicely done
more examples:
通过仔细的观察，我们可以知道一个人的喜好 By observing carefully, we can know a person's preferences  (观察 is a noun here)
他仔细地观察，不错过任何蛛丝马迹 He observes carefully and does not miss any clues (观察 is a verb here)
需要观察得很仔细，才能够分辨出两者有何不同 Need to observe carefully to be able to tell the difference between the two
Note: in contemporary and unofficial writing nowadays, you may find out more people to use 的 instead of 地 or 得 in those specific situations. e.g. 做的好！/ 悄悄的离开了 / 悄悄的来到我身边 which are however grammatically inaccurate but somehow accepted by the public. If you google it, tons of people are actually using it with lots of examples that you can find it online and therefore it has become a norm nowadays.
more reference for 的/地/得 usage here