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I imagine this is something that Japanese speakers naturally build up as they are exposed and communicate in the language for many years. However, take the following scene:

「おお、豪華な魚料理だなぁ」

「港町だけあって魚がやっぱり自慢みたい」- From context this is clearly not referring to the speaker or listener.

「それと地酒も集まるからそっちも沢山」

「お酒か……普段はあんまり飲まないけど、それならたまには……」 - Speaker

「ああ、いただくとしよう」- Speaker

「それじゃ、かんぱーい」

(they all get drunk and have a hang over and get woken up the next
morning)

「朝ーーーーー！」

「ほらほら、みんな起きてー！」

「うう……頭痛い……」- SPeaker

「私も、です……」- Speaker

「少し昨日は、飲み過ぎたな……」- Ambiguous? The speaker (at the bare minimum) is saying that they drank too much yesterday, however they could also be saying "We" drank too much. How does one differentiate between these? Would the wording be slightly different or could the same wording be used for I/You/We?

「普段あまり飲まないからなぁ……加減が分からなくなってしまった」I guess that this is referring to the speaker as it is the same person as before who said they don't drink very much

Would the wording be slightly different or could the same wording be used for I/You/We?

If you're lucky, the choice of a sentence-ending can be an indicator of the subject. For example, the subject of 昨日は飲み過ぎたんでしょう would only be "you" or "you guys", because it doesn't make sense to use でしょう referring to the speaker themselves.

In this case, however, the subject of 少し昨日は飲み過ぎたな is indeed somewhat ambiguous. It can be "I", "we" or "you guys". If the context clearly indicates the speaker did not drink (e.g., the speaker is a teenager boy who was not in the yesterday's party), then the subject would be "you guys". Otherwise, it would be either "I" or "we", and the difference is not important here. If the singular-plural distinction were important, he would have added either 俺は or みんな.

Regarding the last line, 普段あまり飲まない probably applies only to the speaker of this line, so the subject of 加減が分からなくなってしまった should be the same, i.e., singular "I".

It's hard to generalize, but both context and word choice are critically important to determine an implied subject. For example, an honorific verb can automatically indicate the subject is higher than you.