1. This little magic word of two letters is different from all other prepositions because it can be either part of the infinitive or a preposition to take the gerund:
I used to smoke.
I am used to smoking
"To" used with the infinitive is a prospective view i.e. looks forward in time.
I want (1) to go (2) home.
"To" used with the gerund is a retrospective view i.e. looking back
Do you object (2) to people smoking (1) at the table?
Then I stopped (1) to smoke (2) a cigarette.
I stopped (2) smoking (1).
Some other verbs like: remember, forget, regret, try, go on (Mary stopped talking about her holiday and went on to tell us about her plans for the next week) behave in the same way. Some people say there is no difference in meaning between:
I started to work.
I started working.
2. Since "To infinitive" is prospective it is theory (no experience). By contrast gerund being retrospective is habitual, factual and implies experience:
To look after children is difficult.
Looking after children is difficult.
3. Drop or do not drop "to" depends upon the number of objects and the sequence of direct and indirect object that follows:
Write sth to sb (with to)
Write sb sth (no to)
4. I am looking forward to seeing you.
There is some contradiction here. Although "look forward to" is anticipative in its meaning it doesn’t take the infinitive because how can you look forward to sth without prior existence of that sth. Similarly you can’t enjoy sth which doesn’t exist before. The trouble is that because the metaphor of spatial orientation and journey (originally Germanic: German saying: da wo Platz ist) is so powerful in English, we can't fail to look at this verb and think of future.
What about "like"?:
I like to drink Italian coffee.
I like drinking Italian coffee.
Things become more confused when "like" is used in the negative:
I don’t like to go to the dentist. (I don’t go)
I don’t like going to the dentist (I go although I don’t like)
The question is why “to" behaves so oddly. It can contrast with the gerund or the present participle. Can "to" be classified as a preposition and part of the infinitive as in some grammar books? Is it because it has the highest frequency (of Germanic origin) which makes the bare or split infinitive possible or drop it as in informal communication? Is it being degraded under US influence? Why do we keep it in: “I said to him. I spoke to her" but drop it in “I told him. I rang her." There are more words which pair with "to" than with other prepositions. Could this odd behaviour lie in its meaning of reference which can be forward (prospective anticipative = infinitive: implying theory) or backward retrospective / factual / habitual = gerund: implying experience).