The textbook trap: 很 is not "very"
Every beginner textbook translates 很 as "very", and every learner then translates 我很忙 as "I am very busy". To native ears, 我很忙 just means "I am busy". Chinese adjectives cannot stand alone as predicates; they need a connector. 很 is the default colorless connector. To actually say "very busy" emphatically, Chinese speakers stress 很 with tone and volume, or use 非常 (fēicháng, truly) or 特别 (tèbié, especially).
太 always implies excess
太 marks a degree that goes beyond the desirable. 太贵了 (too expensive) is a complaint; 太冷了 (too cold) is a complaint. Rarely, 太 pairs with a positive adjective as hyperbole: 太好了 (great! or literally "too good"), 太棒了 (awesome!). In those cases, the excess is ironic or celebratory. In all other uses, 太 signals that the speaker wants less of whatever quality is being described.
这件衣服很好看,但是太贵了。
Zhè jiàn yīfu hěn hǎokàn, dànshì tài guì le.
This piece of clothing looks nice, but it is too expensive.
Structure: 太 + adjective + 了
太 almost never appears without 了 at the sentence end (at least in positive-form sentences). 太贵 by itself sounds truncated; Chinese speakers finish with 了. The exception is negated 太: 不太贵 (not too expensive) drops the 了 because there is no excess to emphasize. 很 has no 了 requirement; 很贵 stands fine on its own.
这个房间不太大,但是很舒服。
Zhè ge fángjiān bú tài dà, dànshì hěn shūfu.
This room is not too big, but it is quite comfortable.
When 很 becomes emphatic
Stressing 很 in speech (higher pitch, longer duration) turns it into the emphatic "very". In writing, the same effect comes from swapping 很 for 非常, 特别, 挺, or 超. 我很累 is "I am tired"; 我非常累 is "I am exhausted"; 我特别累 is "I am especially tired". Use these when you actually want emphasis; reserve 很 as the grammatical filler.