doing sth. 一般是正在进行时，或将来。（也有些是正在进行时表将来的）而diong sth. 前面要在sb.（某人）后面加be动词（am\is\are） 而to do sth.不用。
对于实用性动词,to do 表示尚未完成,或将要做；doing 表示 已经完成
比如 remenber to do sth 记得要做什么事,remenber doing sth 记得做过什么事
这一类的词语还有forget、stop、regret、try、mean、propose、go on
对于 like /love/hate/ prefer 等词语,to do 表示具体行为；doing sth 表示抽象、倾向概念
例：I like playing basketball,but I don't like to play it today.
对于 need, want, deserve 等词,动名词表被动意义同义于不定式被动态.
例: My bicycle needs repairing = My bicycle needs to be repaired
对于感官动词 see、watch等,doing表示正在发生的事,to do表示整个过程（to要省略）
例：I saw him dancing. 我看见他正在跳舞.(表示看的瞬间）
I saw him dance. 我看见他跳舞（整个过程）
对于finish、 enjoy、consider、imagine、keep、dely、mind、practise、suggest、risk、quit在一般情况下都只能用 doing.
主动句中有些动词+宾语+to do，这类动词除以下外还有advise, allow, believe, cause, command, enable, encourage, entitle, force, invite, order, persuade, remind, show, teach, tell.
例：The police warned everyone to stay inside with their windows closed. （不能The police warned to stay...）
其它动词则不能在to do前放宾语，比如agree, consent, fail, hope, manage, offer, pretend, refuse, start, threaten, volunteer
例：We've decided to leave early. （不能是We've decided us to leave early.）
有些动词后面，宾语+to do前面必须放介词，通常是for，这类动词有advertise, campaign, long, plan, wait，注意在apply和campaign后面的to do通常用被动
例：They arranged for Rania to stay in London. （不能是They arrenged Rania to stay...）
They applied for the court appearance to be postponed.
其它动词可以后接各种介词+宾语+to do。例如
at+宾语+to do (go on《译为持续数落》，keep on, scream, shout, yell)
例：I shouted at the man to open the door.
on+宾语+to do (call《译为正式要求某人做某事》，count, depend, prevail, rely)
例：We're depending on you to find a solution soon.
to+宾语+to do（appeal, gesture, motion, signal）
例：He closed the door and signalled to the pilot to take off.
动词后面还可以跟其它的to do和doing形式
动词+否定to do和否定doing
例:We decided not to go to Paris after all.
Some of my friends have considered not going to college because of the cost.
动词+to have+过去分词，这种形式通常是用在对过去发生的某件事提供意见（尤其是和seem和appear连用），或者报到过去发生的事件（通常跟动词被动式is/was alleged, believed, said, thought）
例：The accident seems to have happened at around 1 pm yesterday.
Simmons is alleged to have assaulted a police officer.
动词+having+过去分词，常见于admit, deny, forget, recall, regret和remember，和动词+doing意思相近
例：I now regret buying the car=I now regret having bought the car.
这个需要记忆一些固定词组以及在特定情况下区分意思或者是时态
嘿嘿嘿嘿，这个让我想起了我初中时候经常背的，很有意思！
这个主要是自己记住，背下来，有的是只加to do 形式，有的只能加doing，有的词后面既可以加to do 有可以加doing sth，这都是固定搭配。你背下来就是了