find sth doing/ find sb doing/ find sth done是什么用法？

这两种用法都是对的，但所表达的语意不同

find sth doing
发现...处于某种状态

find sth. done.
发现某事被完成了
这里的done是宾语补足语

给你一道题

This morning after I got up, I found my bike ____.
A. miss B. missed C. misses D. missing

发现、发觉（某人某物处于某种状态或在做某事）
find sb doing sth
应该选D选项，处于丢的状态。

miss 
　　［误］ I found my bag missed.
　　［正］ I found my bag missing.
　　［析］ missing为形容词，其意为"不见了"、"丢了"。在句中用作宾语补足语时不要误用missed，它作动词时多为及物动词，要接名词或动名词，而不接不定式。如： I missed the first train, I don't want to miss seeing the famous football player.在作补足语讲某物"不见了"时有missing, gone, lost等，如： I found my bag missing (gone, lost).

扩展阅读：find it adj to do sth ... give sth back to sb ... be used to doing ... take turns in doing sth ... feel sb doing sth ... find it adj doing ... find ones way ... find doing something ... find sb adj ...