The girl I spoke to was my cousin
这是什么句子，为什么能这样写，请大师举一反三，并说明此举子的包含的语法知识！谢谢！

The girl (I spoke to ) was my cousin.
(I spoke to) 是定语从句，修饰主语the girl. 这里省略了关系代词：that/whom/who
完整句子是： The girl that/whom spoke to was my cousin.
先行关系代词whom/tha/whot是从句的宾语.

可以这样理解：
The girl was my cousin.那女孩是我堂姐（妹）。
哪个女孩？（也许有好几个女孩在一起）
原来是： that/whom I spoke to 我对她讲话的那个。

理解这类句子，你需要"先找句子的主干：即主语，谓语和宾语
或者主系表结构"等等。
主语：the girl
系表：was + my cousin

补充：
关于你的补充问题，摘录一些如下，希望帮到你：
【关系代词的不可省略和可以省略】

1.关系代词which,whom,who,that在定语从句中作宾语时可以省略。
Here is the man (who/that/whom)you're been looking for.

以下情况不能省略：

（1）在介词+whom与介词+which中，whom,which不能省略。
Do you know any shops nearby in which I can buy flowers?
That is the headmaster with whom my father was talking just now.
注：当介词放在动词后时，which,whom就可以省略。
Who is the man (whom) you talked with just now?

（2）在非限制性定语从句中，作宾语的关系代词也不能省略。
Mr Green,whom you know,is the tallest in our school.
The elephant is like a spear,as anybody can see.

（3）在the same ...as,such...as,as...as,the same...that中，as,that即使作宾语，也不能省略I have bought the same bicycle as you have (bought). (指同类用as)
This is the same book that I read the day before yesterday. (that指同一个)

（4）当由and,but,or等连词连接两个或两个以上的定语从句修饰一个先行词时，第一个关系代词可省，但第二，第三个不可省略。
This is the book (which) I read yesterday and which I find very interesting.

2.当that在从句中作补语时可以省略。
He is not the man (that) he used to be.
She is all (that) a teacher should be.

3.在there be 结构中出现定语从句，或在定语从句中出现there be 时，用作主语的关系代词也可省略。
There is a man downstairs (who) wants to see you.
This is the best dictionary (that) there is in the library.

4.状语的省略

（1）当先行词是reason，而且定语从句中作原因状语时，关系代词可用why,that,也可以省略。
The reason (why/that) he failed was his laziness.
That is the reason (why) I did it.

（2）当先行词是way,且在定语从句中作方式状语时，关系代词可用in which,that,也可以省略。
The way (in which/that) these comrades look at problems is wrong.
That was the way (in which/that) she worked the problem out.
注意：当关系代词在定语从句中作主语时，不省略。
例如：I don't know the way that/ which leads to the top of the mountains.

(3)当先行词是time时，关系代词可用when,that 或省略。
The second time (that) I saw him was in 1980.
I don't know the exact time (when/that) the sports meet will take place.
注意：关系代词作宾语有时也不能省略。