look up 一般指在字典里查找单词什么的,
look up the word in the dictionary.
look for 指寻找,更倾向于找的过程,动作,（顺便提一下）
find也是寻找,但更倾向于结果.
I looked (look的过去式）for my shoes ,but I couldn't find them .
look over 多指检查,考试检查之类的
Please look over your exam paper carefully.
look at 看,瞧.更倾向于看的动作,（顺便提一下）,see也是看,但倾向于结果.
I look at the blackboard,but I can't see anything.
顺便提一下,所有的词组百度里查一下都能找到,我的是中小学生经常用的,常见的简单语法点.