For

for 经常的使用方法是告诉我们something的用途，比如说原因或者目的。

For usually tells us about the use of something, a reason or purpose.

We need new batteries for the remote control.

These drinks are for after work.

We use it for cutting grass.

Of

Of经常是展示一种所属关系或者联系

Of usually shows a connection or belonging.

Is she a friend of yours?

This is a photo of my wife.

A glass of wine.

To

To经常是展示something的方向，向哪里移动。

To usually shows the direction of something; moving towards.

We're going to Malta next week.

Where are you going to buy your new shoes?

We ran to the end of the street.

辨析

for和to都可以接目的，他两的区别在于，for只是表示something的目的，但是没有行动，to有一种正在向这个目的的一个趋势
比如说这个句子She walks ___ work every day.如果填写for的话表示他寻求一个工作，但是不可能是每天寻求工作，所以填写to表示他每天都走路去工作。
on和for 的辨析，on business 意思是从事business,on is engaged in,for business意思是为了商业的目的for is Having (the thing mentioned) as a purpose or function.
例句：Susan was called out of town on business.一般是用on表示从事商业活动，而用for的话有一种诉求在里面，感情太过了（表示这个人功利心很重）on的话表示选择了一种职业。
on和of的辨析,"Some variations on the activity" vs "Some variations of the activity". variations of means "instances of a changed thing", variations on usually means "a thing [usually a musical theme] with small modifications" on 和of的辨析还是要看具体的词的用法，对于variations这个词来说，variation on sth意思是sth的一个小改动，variation of sth 意思是一个改变了sth的一个变体，区别在于改动的大小，of的话改动是比较大的，on的话是一个小的改变。

for的用法

介词for的用法

(1) 表示动作的目的,意图或利益,可翻译为”为……”

I want to go back for my pen.

我要回去拿我的钢笔.

Let’s go for a walk.

我们去散步吧.

Smoking is not good for the health.

吸烟有害健康.

(2) 表示用途,意为”适用于,适合,给”

Here are some bags for sports.

这里有许多运动包.

This is a book for children.

这是一本适合孩子读的书.

(3) 表示动作的方向,目的地,意为”向…….,往……”

He left for shanghai last week.

他上周出发去了上海.

This ship is for [NY.]

这艘船是开往纽约的.

(4) 表示时间,距离

We will stay there for two weeks.

我们会在那里待两周.

I usually walk for two hours.

我经常散步两小时.

（5) 表示原因,理由,常与”thank, famous连用”

Thank you for your help.

谢谢你的帮助.

Jackie chan is famous for his movie.

成龙因为他的电影而著名.

(6) 表示赞成,支持,反义词为”against”

Are you for the plan or against it?

你是支持这个计划还是反对它?

(7) 用在一些固定搭配中

look for 寻找

wait for 等待

be late for 迟到